NCERT Class 12 Maths
Chapter 9: Differential Equations
19 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations — Exercise 9.5
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Solve y′+\(2\) y=\(\sin{\left(x \right)}\).
Question 2
Solve y′+\(3\) y=\(e^{- 2 x}\).
Question 3
Solve y′+\(\frac{1}{x}\) y=\(x^{2}\).
Question 4
Solve y′+\(\sec{\left(x \right)}\) y=\(\tan{\left(x \right)}\).
Question 5
Solve y′+\(\sec^{2}{\left(x \right)}\) y=\(\tan{\left(x \right)} \sec^{2}{\left(x \right)}\).
Question 6
Solve y′+\(\frac{2}{x}\) y=\(x \log{\left(x \right)}\).
Question 7
Solve x log x·y′+y=(2/x)log x, with the original real-log domain x>0.
Question 8
Solve y′+\(\frac{2 x}{x^{2} + 1}\) y=\(\frac{\cot{\left(x \right)}}{x^{2} + 1}\).
Question 9
Solve y′+\(\cot{\left(x \right)} + \frac{1}{x}\) y=\(1\).
Question 10
Solve x′+\(-1\) x=\(y\).
Question 11
Solve x′+\(\frac{1}{y}\) x=\(y\).
Question 12
Solve x′+\(- \frac{1}{y}\) x=\(3 y\).
Question 13
Solve y′+\(2 \tan{\left(x \right)}\) y=\(\sin{\left(x \right)}\). Given y(\(\frac{\pi}{3}\))=\(0\).
Question 14
Solve y′+\(\frac{2 x}{x^{2} + 1}\) y=\(\frac{1}{\left(x^{2} + 1\right)^{\frac{3}{2}}}\). Given y(\(1\))=\(0\).
Question 15
Solve y′+\(- 3 \cot{\left(x \right)}\) y=\(\sin^{2}{\left(x \right)}\). Given y(\(\frac{\pi}{2}\))=\(2\).
Question 16
Find the curve through the origin whose tangent slope equals the sum x+y of its coordinates.
Question 17
Find a curve through (0,2) whose coordinate sum exceeds the magnitude of its tangent slope by 5.
Question 18
Find an integrating factor of xy′−y=2x².
Question 19
Find an integrating factor for (1−y²)dx/dy+yx=ay, −1<y<1.