Question Text
Question 2 :
Solve the differential equation: $\displaystyle x\left ( x-1 \right )\frac{dy}{dx}-\left ( x-2 \right )y= x^{3}\left ( 2x-1 \right ).$
Question 3 :
Solve the differential equation: $\displaystyle \left ( 1-x^{2} \right )\frac{dy}{dx}-xy= \frac{1}{\sqrt{\left ( 1-x^{2} \right )}}$
Question 4 :
For the differential equation $\displaystyle x\left ( 1-x^{2} \right )dy+\left ( 2x^{2}y-y-ax^{3} \right )dx= 0.$ If y(1)=0 then the value of the constant is <br>
Question 5 :
An integrating factor of the differential equation $x\cfrac { dy }{ dx } -y={ x }^{ 3 };x>0$ is ______
Question 6 :
The integrating factor of the differential equation $\dfrac {dy}{dx} = \dfrac {1}{x + y + 2}$ is
Question 7 :
Solve for differntial equation: $\displaystyle \left ( x^{3}-x \right )\frac{dy}{dx}-\left ( 3x^{2}-1 \right )y= x^{5}-2x^{3}+x$
Question 8 :
The solution of $\dfrac { dy }{ dx } +3{ x }^{ 2 }y={ x }^{ 5 }{ e }^{ { x }^{ 3 } }$ is
Question 10 :
The solution of the differential equation $\displaystyle \frac { dy }{ dx } ={ e }^{ y+x }+{ e }^{ y-x }$ is
Question 11 :
<span>The Integrating Factor of the differential equation<br></span><span>$\left(1-y^{2}\right) \cfrac{d x}{d y}+y x=a y(-1<y<1) \text { is }$</span><br>
Question 12 :
Solution of the differential equation $\dfrac{dx}{dy}-\dfrac{x \log x}{1+\log x}=\dfrac{e^{y}}{1+\log x}$ if $y(1)=0$, is
Question 16 :
The solution of the differential equation $\quad  y '=\cfrac { 1 }{ { e }^{ -y }-x } $ is:
Question 17 :
The solution of the differential equation <br>$\cfrac { ydx+xdy }{ ydx-xdy } =\cfrac { { x }^{ 2 }{ e }^{ xy } }{ { y }^{ 4 } } $ satisfying y(0) = 1, is <br>
Question 20 :
Solution of the differential equation $\dfrac { dy }{ dx } $ $=\sin (x+y)+\cos(x+y)$ is
