Question 1 :
The order and degree of the differential equation $\sqrt { \dfrac { dy }{ dx } } -4\dfrac { dy }{ dx } -7x=0$ are
Question 3 :
Solve $\displaystyle \left ( 4x+6y+3 \right )dx= \left ( 6x+9y+2 \right )dy$
Question 5 :
The solution of the differential equation ${e^{ - x}}(y + 1)dy + (co{s^2}x - sin2x)ydx = 0$ subject to the conditions $y(0) = 1$
Question 7 :
Degree and order of the differential equation $\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ={ \left( \dfrac { dy }{ dx } \right) }^{ 2 }$ are respectively
Question 8 :
The degree of the differential equation<br>$\displaystyle { \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ { 5 }/{ 3 } }=\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } $<br>
Question 11 :
Check whether the function is homogenous or not. If yes then find the degree of the function<br/>$g(x)=8x^4$.
Question 12 :
Which of the following is true regarding the function $f(x, y)= x^4 \sin \dfrac{x}{y}$ ?
Question 13 :
Solve the differential equation$\displaystyle x\frac{dy}{dx}= y\left ( \log y-\log x+1 \right )$
Question 16 :
The order and degree of the differential equation $\displaystyle\frac{d^2y}{dx^2}=\sqrt[3]{1-\displaystyle\left(\frac{dy}{dx}\right)^4}$ are respectively.
Question 20 :
Solve the differential equation $\displaystyle e^{dy/dx}=x+1$ given thet when $\displaystyle x=0,y=3.$
Question 21 :
Check whether the function is homogenous or not. If yes then find the degree of the function<br/>$g(x)=4-x^2$.
Question 22 :
The solution of the differential equation $ x \dfrac {dy}{dx} = \dfrac {y}{1 + \log x } $ is :
Question 24 :
Check whether the function is homogenous or not. If yes then find the degree of the function<br/>$g(x)=x^2-8x^3$.<br/>
Question 26 :
Find the value of $k$ for the function: $2x^2y+3xyz+z^k$ to be homogenous.
Question 27 :
The solution of $\cfrac { dy }{ dx } =\cfrac { y }{ x } +\tan { \cfrac { y }{ x }  } $ is:
Question 28 :
Solve the differential equation:  $\displaystyle x\sin  \left( \frac { y }{ x }  \right) dy=\left( y\sin  \left( \frac { y }{ x }  \right) -x \right) dx$
Question 29 :
The order and degree of $\dfrac{d^{2}y}{dx^{2}}+\sqrt{1+\left ( \dfrac{dy}{dx} \right )^{3}}=0$ is:
Question 31 :
Solution of the differential equation $ydx+x\log { \left( \frac { y }{ x } \right) dy-2xdy=0 }$ is
Question 32 :
The degree and order of the differential equation of the family of all those parabola's whose axis is $x$-axis are respectively.<br>
Question 33 : <p>The solution of the differential equation $ ({x^2} - {y^2})dx + 2xy\,dy = 0$</p>
Question 34 :
The solution of the differential equation $\dfrac { dy }{ dx } =\dfrac { x-2y+1 }{ 2x-4y }$
Question 36 :
The differential equation representing the family of curves $\mathrm{y}^{2}=2\mathrm{c}(\mathrm{x}+\sqrt{\mathrm{c}})$, where $\mathrm{c} >0$, is a parameter, is of order and degree as follows: <br/>
Question 37 :
The differential equation $ \dfrac{dx}{dy} $ = $ \dfrac{1}{ax + by + c} $, where a, b, c are all non zero real numbers, is
Question 38 :
The order and degree of the differential equation $(y''')^2 + (y'')^3 - (y')^4 + y^5 = 0$ is
Question 40 :
If $\displaystyle x\frac{dy}{dx}=y(\log y -\log x+1)$ then the solution of the equation is:
Question 42 :
The solution of the equation $\cfrac{dy}{dx}=\cfrac{y}{x}\left( \log { \cfrac { y }{ x } } +1 \right) $ is
Question 44 :
Find the equation of the curve with D.E. $(1+y^{2})dx=xydy$, and passing through $(1, 0)$.<br/>
Question 46 :
General solution of differential equatin $\dfrac{dy}{dx} + y = 1 (y \neq 1)$ is:
Question 47 :
$\displaystyle (x^{2}-y^{2})dx+2xy dy=0$,  the solution to this differential equation represents which curve:
Question 48 :
The order and degree of D.E $\left[ 1+\left( \dfrac { dy }{ dx }  \right) ^{ 2 } \right] ^{ 3/2 }=8\dfrac { { d }^{ 2 }y }{ dx^{ 2 } } $ is:<br/>
Question 51 :
The order and degree of  $\left ( \dfrac{d^{2}y}{dx^{2}} \right )^{1/3}=10+9x\dfrac{dy}{dx}$ is:
Question 52 :
The order and degree of the differential equation of all parabola whose axis is x-axis<br>
Question 53 :
<span>Find the order and degree of </span>$\left [ \displaystyle \frac {d^2x}{dt^2} \right ]^3\, +\, \left [ \displaystyle \frac {dx}{dt} \right ]^4\, -\, xt\, =\, 0$.
Question 57 :
If $\displaystyle \frac{\mathrm{d} y}{\mathrm{d} x}= \frac{x-y}{x+y}$ and $y\left ( 1 \right )= 1$ then $y\left ( 2 \right )$ equals
Question 58 :
The solution of the differential equation $\displaystyle \frac{dy}{dx}=\frac{x+y}{x}$ satisfying the condition $y(1)=1$ is:<br/>
Question 59 : <p>The degree and order of<br/>the differential equation ${\left[ {1 + 2{{\left( {\dfrac{{dy}}{{dx}}} \right)}^2}} \right]^{1/2}} = 5\dfrac{{{d^2}y}}{{d{x^2}}}\,\,are\,$</p>
Question 60 :
The order and degree of $\left [ 1+\left ( \dfrac{dy}{dx} \right )^{2} \right ]^{3/2}=\left ( \dfrac{d^{2}y}{dx^{2}} \right )^{2}$ is:<br/>
Question 68 :
The order and degree of the differential equation of the family of the circles touching the $x$-axis at the origin, are respectively:
Question 69 :
The general solution of differential equation is$\left ( y+c \right )^{2}=cx$ where $c$ is an arbitrary constant. The order and degree of the differential equation are respectively:
Question 70 :
The order and degree of D.E $\left [ 1+\dfrac{d^{3}y}{dx^{3}} \right ]^{1/3}=\dfrac{d^{2}y}{dx^{2}}$ is:
Question 72 :
The differential equation whose solution is $Ax^{2}+By^{2}=1$, where A and B are arbitrary constants is of<br>
Question 73 :
Solution of the equation $\displaystyle xdy=\left( y+x\frac { f\left( y/x \right) }{ f'\left( y/x \right) } \right) dx$ is
Question 76 :
By substituting $x=vy$ the transformed equation of $(1+e^{x/y})dx+e^{x/y}\left ( 1-\frac{x}{y} \right )dy=0$ is
