RD Sharma Class 12 Exercise 21.2 Differential Equation Solutions Maths-Download PDF Online
RD Sharma Class 12 Exercise 21.2 Differential Equation Solutions Maths-Download PDF Online
Edited By Satyajeet Kumar | Updated on Jan 24, 2022 04:19 PM IST
Class 12 students face regular tests and exams to test their understanding ability of almost every concept they learn. This requires regular practice in the right manner. Topics like Differential equations in mathematics are always challenging for high school students. Students must have the RD Sharma Class 12th Exercise 21.2 to have clarity in this chapter and attend those sums without any doubts. Not only do students use these solution books, many teachers and tutors also do to recheck their answers and find easier methods to solve the sums.
Answer: Hint: Differentiating given equation with respect to x [Applying log both sides] Given: Solution: We have, Hence, is the differential equation corresponding to
Answer: Hint: Differentiating the given equation with respect to x Given: Solution: On differentiating with respect to x, Substituting the value of a, we get Hence, is the differential equation corresponding to
Answer: Hint: Differentiating the given equation, let it equation (i) and substitute a from (iii) in (ii) Given: Solution: Again, Substitute equation (iii) in (ii),
Answer: Hint: Differentiating the given equation with respect to x Given: Solution: Differentiating with respect to x Putting the value of a in the given equation, we get put
Answer: Hint: Differentiating the given equation where r is a constant Given: Solution: From equation (ii) Put this value in equation (i) Squaring equation (iii), Dividing equation (iv) by (v),
Answer: Hint: Let (0, k) be the centre of the circle with k as its centre and differentiating the equation of the circle Given: Circles pass through origin and their centre lie on y-axis Solution:
Answer: Hint: Let the equation of the circle assuming R as radius and (a,b) as the centre of the circle is Given: Circles passes through origin and their centre lie on x-axis. So the centre of the circle will be (a, 0) Solution: Substituting these values in equation (i)
Answer: Hint: Let the surface be A Rate of evaporation, Using formula, Given: Rain drop evaporates at a rate proportional to its surface area Solution:
Answer: Hint: Let the equation of parabola be Where h, k are parameter Given: Latus rectum 4a and axis are parallel to x-axis Solution: Let the equation of parabola be Where h, k are parameter which is the required differential equation.
Answer: The required equation is Hint: The given equation is the equation of a circle Given: Solution: Differentiating with respect to x, The required equation is
Answer: The required equation is Hint: Differentiating the given equation with respect to x Given: Solution: Differentiating with respect to x, The required equation is
Answer: The required differential equation is Hint: Given: Solution: The equation of family of curves is Where b is a parameter Differentiating equation (i) with respect to x, we get The required equation is
Answer: The required differential equation is Hint: Differentiating equation (i) with respect to x Given: Solution: The equation of family of curves is Where a is a parameter Differentiating equation (i) with respect to x, we get The required equation is
Answer: The required differential equation is Hint: This is the equation of hyperbola Given: Solution: The equation of family of curves is Where a and b are parameter Differentiating equation (i) with respect to x, we get Differentiating equation (ii) with respect to x, we get Now, from (ii), we get From (iii) and (iv), we get The required differential equation is
Answer: The required differential equation is Hint: Differentiating equation (i) and (ii) with respect to x Given: Solution: The equation of family of curves is Where a and b are parameters Differentiating equation (i) with respect to x, we get Differentiating equation (ii) with respect to x, we get The required differential equation is
Answer: The required equation is Hint: Differentiating the given equation with respect to x Given: Solution: On differentiating with respect to x, we get From the given equation, So, we have The required equation is
Answer: The required equation is Hint: Differentiating the given equation with respect to x Given: Solution: Differentiating with respect to x, The required equation is
Answer: The required equation is Hint: Differentiating the given equation with respect to x Given: Solution: Differentiating with respect to x From the given equation, we have Now, The required equation is
Answer: The required differential equation is Hint: Ellipse centre at the origin and foci on the x-axis Given: Ellipse having the centre at the origin and foci on the x-axis Solution: Equation of required ellipse is Where a and b are arbitrary constants Differentiating equation (i) with respect to x, we get Differentiating equation (ii) with respect to x, we get The required differential equation is
Answer: The required differential equation is Hint: Hyperbola centre at the origin and foci on the x-axis Given: Hyperbolas having the centre at the origin and foci on the x-axis Solution: Equation of required ellipse is Where a and b are arbitrary constants Differentiating equation (i) with respect to x, we get Differentiating equation (ii) with respect to x, we get Substituting this value of 1/a2 in equation (ii), we get The required differential equation is
Answer: The required differential equation is Hint: The equation belongs to the family of a circle Given: The family of circles in the second quadrant and touching the co-ordinate axes Solution: Let c denotes the family of circles in the second quadrant and touching the coordinate axes and let(-a,a) be coordinate of the centre of any member of this circle Now, the equation representing this family of circle is Differentiating (ii) with respect to x, we get Substituting this value of a in (i), we get The required differential equation is
Answer: The required differential equation is Hint: Differentiating the given equation with respect to x Given: Solution: Where a and b are arbitrary constants Differentiating with respect to x Again, Differentiating with respect to x Put from (i) and (ii) in equation (iii), we get The required differential equation is
Answer: The required differential equation is Hint: Differentiating the given equation with respect to x Given: Solution: Differentiating with respect to x, we get Putting (i) in (ii) Again, Differentiating with respect to x, we get Putting (iii) in (iv), we get The required differential equation is
Chapter 21, Differential Equation of class 12, is a portion where most of the students lose their marks. This chapter consists of eleven exercises, ex 21.1 to ex 21.11. this seconds exercise, ex 21.2, contains 27 sums to be solved. The concepts involved in this exercise are solving the differential equations in various forms. Even though the entire chapter has the same concept, the method by which each sum is solved varies greatly. Therefore, the use of RD Sharma Class 12 Chapter 21 Exercise 21.2 becomes essential to make the students understand each method without being confused by one another.
There is no other option than to practice the whole set of sums multiple times. The top-rated reference book, the RD Sharma Class 12th Exercise 21.2, comes with numerous practice questions for the students to work out. The more sums they practice in differential equations, the better they understand the concept in-depth. With the latest questions updated according to the NCERT syllabus, the Class 12 RD Sharma Chapter 21 Exercise 21.2 Solution is the best reference guide. For the sums that have various possible methods given in this book, students can select the ones that they feel to adapt.
Many teachers use the RD Sharma Class 12 Solutions Differential Equation Ex 21.2 reference material to frame their question papers. When the students practice with this book beforehand, they eventually face the questions easily during their tests and exams. RD Sharma solutions As the most suggested solution book by the previous bath students, the RD Sharma Class 12th Exercise 21.2 is popular among the class 12 students.
The best part of owning an RD Sharma book is that it is available for free of cost at the Career 360 website. Anyone can download the RD Sharma Class 12 Solutions Chapter 21 Ex 21.2 from the Career 360 website directly without wanting to pay even a penny. Many students who use these books for their exam preparation have admitted that their test scores have improved. Now, it is your turn to prepare for our grade 12 public exam with the RD Sharma books.
1.Which reference books are very much helpful for the students who struggle with the chapter Differential Equation?
The RD Sharma Class 12th Exercise 21.2 reference book is the best guide for the students who are unclear about the sums in the Differential Equation chapter.
2.Where can the students find the RD Sharma books that can be accessed without payment?
Everyone can access the RD Sharma books at the Career 360 website without any payment.
3.How can a student improve their ability to solve the Differential Equation sums without any mistakes?
Practice is the best way that a student can follow to understand the sums in the Differential Equation chapter. They can use the RD Sharma Class 12th Exercise 21.2 solution material to guide them through this process.
4.What is the most common reference guide for class 12 mathematics used by the CBSE board school students?
The CBSE board school students' most preferred and used mathematics guide is that of the RD Sharma collections.
5.How many questions should a student solve for chapter 21 in class 12 mathematics?
There are 27 questions of chapter 21; mathematics asked in the textbook; along with these questions, the students must work out more additional sums to gain practice.