NCERT Class 12 Maths
Chapter 9: Differential Equations
17 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations — Exercise 9.4
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Show the equation y′=\(\frac{x^{2} + y^{2}}{x^{2} + x y}\) is homogeneous and solve it.
Question 2
Show the equation y′=\(\frac{x + y}{x}\) is homogeneous and solve it.
Question 3
Show the equation y′=\(\frac{x + y}{x - y}\) is homogeneous and solve it.
Question 4
Show the equation y′=\(\frac{- x^{2} + y^{2}}{2 x y}\) is homogeneous and solve it.
Question 5
Show the equation y′=\(\frac{x^{2} + x y - 2 y^{2}}{x^{2}}\) is homogeneous and solve it.
Question 6
Show xdy−ydx=√(x²+y²)dx is homogeneous and solve.
Question 7
Show the equation y′=\(\frac{y \left(x \cos{\left(\frac{y}{x} \right)} + y \sin{\left(\frac{y}{x} \right)}\right)}{x \left(- x…
Question 8
Show the equation y′=\(- \sin{\left(\frac{y}{x} \right)} + \frac{y}{x}\) is homogeneous and solve it.
Question 9
Show the equation y′=\(- \frac{y}{x \left(\log{\left(\frac{y}{x} \right)} - 2\right)}\) is homogeneous and solve it.
Question 10
Show (1+e^(x/y))dx+e^(x/y)(1−x/y)dy=0 is homogeneous and solve.
Question 11
Show the equation y′=\(\frac{- x + y}{x + y}\) is homogeneous and solve it. Initial condition: y(1)=1.
Question 12
Show the equation y′=\(\frac{- x y - y^{2}}{x^{2}}\) is homogeneous and solve it. Initial condition: y(1)=1.
Question 13
Show the equation y′=\(- \sin^{2}{\left(\frac{y}{x} \right)} + \frac{y}{x}\) is homogeneous and solve it. Initial condition: y(1)=π/4.
Question 14
Solve y′−y/x+cosec(y/x)=0 with y(1)=0.
Question 15
Show the equation y′=\(\frac{y}{x} + \frac{y^{2}}{2 x^{2}}\) is homogeneous and solve it. Initial condition: y(1)=2.
Question 16
To solve dx/dy=h(x/y), which substitution is appropriate?
Question 17
Which differential equation is homogeneous?