CBSE CLASS 12 DIFFERENTIAL EQUATION (HOMOGENEOUS) PRACTICE QUESTIONS

HOMOGENEOUS DIFFERENTIAL EQUATION PRACTICE QUESTIONS 

1.   Solve the differential equation $$x^{2}dy+y\left(x+y\right)dx=0$$ given that y=1 when x=1.

2.   Solve the differential equation
$\left(x+y\right)dy+(x-y)dx=0,giventhaty=1whenx=1.$

$$3.   Solve $x^{2}ydx-\left(x^3+y^3\right)dy=0$

$$4.   Find the particular solution of the differential equation:
  $\left(x^2+xy\right)dy=\left(x^2+y^2\right)dxgiventhaty=0whenx=1.$

$$5.   Solve
  $y\left\{x\cos \left(\frac{y}{x}\right)+y\sin \left(\frac{y}{x}\right)\right\}dx-x\left\{y\sin \left(\frac{y}{x}\right)-x\cos \left(\frac{y}{x}\right)\right\}dy=0$

$$6.   Solve: $2y{e}^{\frac{x}{y}}dx+\left(y-2x{e}^{\frac{x}{y}}\right)dy=0$

$$7.   Solve the following initial value problem
(i)   $x\frac{dy}{dx}\sin \left(\frac{y}{x}\right)+x-y\sin \left(\frac{y}{x}\right)=0,y\left(1\right)=\frac{\pi }{2}$
(ii)  $2x^2\frac{dy}{dx}-2xy+y^2=0,y\left(e\right)=e$
(iii)  $\frac{dy}{dx}-\frac{y}{x}+\cos ec\frac{y}{x}=0,y\left(1\right)=0$
$$ (iv)  $\left\{x{\sin }^2\left(\frac{y}{x}\right)-y\right\}dx+xdy=0,y\left(1\right)=\frac{\pi }{4}$

8.Find the particular solution of the differential equation
  $x\cos \left(\frac{y}{x}\right)\frac{dy}{dx}=y\cos \left(\frac{y}{x}\right)+x,giventhatwhenx=1,y=\frac{\pi }{4}$

9.Find the particular solution of the differential equation$$
$\left(x-y\right)\frac{dy}{dx}=x+2y,giventhatwhenx=1,y=0$

$$10.  Find the particular solution of the differential equation $\frac{dy}{dx}=\frac{xy}{x^2+y^2}giventhaty=1\text{w}henx=0$

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