Write the degree of the differential equation \(\left( \frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \right) ^{ 2 }+\left( \frac { ds }{ dt } \right) ^{ 3 }+4=0\)

Write the differential equation formed from the equation y = mx + c, where m and c are arbitrary constants.

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.

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

Find the integrating factor of the differential equation \(\left( \frac { { e }^{ -2\sqrt { x } } }{ \sqrt { x } } -\frac { y }{ \sqrt { x } } \right) \frac { dx }{ dy } =1\) .

From the differential equation of equation y = a cos2x + b sin2x, where a and b are constant.

Solve the differential equation \(\frac { dy }{ dx } =\sqrt { \frac { 1-\cos { x } }{ 1+\cos { x } } } \)

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

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

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

Show that the differential equation x cos \(\left( \frac { y }{ x } \right) \)\( \frac { dy }{ dx }\) = y cos \(\left( \frac { y }{ x } \right) \) + x is homogeneous and solve it.

 Show that the general solution of the differential equation \(\frac {dy}{dx}\)+\(\frac { { y }^{ 2 }+y+1 }{ { x }^{ 2 }+x+1 } =0\) is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.

Verify that the function \(y={ e }^{ -3x }\) is a solution of the differential equation \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +\frac { dy }{ dx } -6y=0.\)

Form the differential equation representing the family of curves \(y=mx,\) where  'm' is an arbitrary constant.

Find the general solution of the differential equation: \(\frac { dy }{ dx } =\frac { 1+{ y }^{ 2 } }{ 1+{ x }^{ 2 } } .\)

Solve: (3xy + y²)dx + (x² + xy) dy =0.

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

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.