Write the degree of the differential equation: \(5x{ \left( \frac { dy }{ dx } \right) }^{ 2 }-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0.\)

Write the degree of the differential equation \({ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+x\left( \frac { dy }{ dx } \right) ^{ 4 }=0\)

Find the differential equation of the family of lines passing through the origin.

Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.

Find the solution of the differential equation \(\frac { dy }{ dx } ={ x }^{ 3 }{ e }^{ -2y }\)

Solve the differential equation \(\frac { dy }{ dx } ={ e }^{ x-y }+x{ e }^{ -y }\).

Solve the differential equation \(\frac { dy }{ dx } =xy+2y\)

Find the general solution of differential equation \(\frac { dy }{ dx } ={ e }^{ 3x-4y }\)

Find the general solution of differential equation \(\log { \left( \frac { dy }{ dx } \right) } =x+1\)

Find the general solution of the differential equation: \((x-y){dy\over dx}={x+2y}\)

Verify that the function y = a cos x + b sin x, where a, b \(\in\) R is a solution of differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0\).

Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x² + 1) dx, (x\(\neq \)0).

Find the equation of the curve through the point,\(\left( 0,\frac { \pi }{ 4 } \right) \) whose differential equation is sin x cos y dx+ cos x sin y dy=0.

Find the equation of a curve passing through the point (0, 0) and whose differential equation is :  \(y'={ e }^{ x }sin x\)

Find the particular solution of the differential equation:\(\left( x-y \right) \left( dx+dy \right) =dx-dy,\) given that \(y=-1\)when \(x=0.\)

Solve the differential equation : \(\left(x^{2}-1\right) \frac{d y}{d x}+2 x y=\frac{2}{x_{2}-1}\)

Solve the differential equation :  \(\frac {dy}{dx}\) + \(\frac {1+cos2y}{1-cos2x}\) =0.

Find the particular solution satisfying the given condition : \({ x }^{ 2 }dy+\left( xy+{ y }^{ 2 } \right) dx=0\); y = 1, when x = 1.

Find the particular solution of the differential equation :
\(x{ e }^{ \frac { y }{ x } }-y\sin { \left( \frac { y }{ x } \right) } +x\frac { dy }{ dx } \sin { \left( \frac { y }{ x } \right) } =0\) for x = 1, y = 0.