NCERT Class 12 Maths
Chapter 9: Differential Equations
12 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations — Exercise 9.2
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Verify y=\(e^{x} + 1\) solves y″−y′=0.
Question 2
Verify y=\(C + x^{2} + 2 x\) solves y′−2x−2=0.
Question 3
Verify y=\(C + \cos{\left(x \right)}\) solves y′+sin x=0.
Question 4
Verify y=\(\sqrt{x^{2} + 1}\) solves y′=xy/(1+x²).
Question 5
Verify y=\(a x\) solves xy′=y, x≠0.
Question 6
Verify y=x sin x for xy′=y+x√(x²−y²), with printed restrictions x≠0 and (x>y or x<−y).
Question 7
Verify xy=log y+C; y′=y²/(1−xy), xy≠1.
Question 8
Verify y−cos y=x; (y sin y+cos y+x)y′=y.
Question 9
Verify x+y=tan⁻¹y; y²y′+y²+1=0.
Question 10
Verify y=\(\sqrt{a^{2} - x^{2}}\) solves x+yy′=0, −a<x<a, y≠0.
Question 11
How many arbitrary constants occur in the general solution of a fourth-order differential equation?
Question 12
How many arbitrary constants occur in a particular solution of a third-order differential equation?