Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 3 }-4\left( \frac { dy }{ dx } \right) \)+y = 3e^x

Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0

Write down the order and degree of the following differential equations.
\(\sqrt { 1+\left( \frac { dy }{ dx } \right) ^{ 2 } } \)= 4x

Write down the order and degree of the following differential equations.
\(\left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 2 }{ 3 } }=\frac { d^{ 2 }y }{ { dx }^{ 2 } } \)

Find the differential equation for y = mx + \(\frac { a }{ m } \) where m is arbitrary constant.

Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

Solve: x dy +y dx = 0

Solve: (x² - ay)dx = (ax-y²)dy

Solve: \(\frac { dy }{ dx } \)+ ay = e^x (where a ≠ -1)

The change in the cost of ordering and holding C as quantity q is given by \(\frac { dC }{ dq } =a-\frac { c }{ q } \) where a is a Constanst. Find C as a function of q.

Solve: 3\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -5\frac { dy }{ dx } \)+ 2y = 0

Solve: (D²-6D+25)y = 0

Form the differential equation of the family of curves y = A cos 5x + B sin 5x where A and B are parameters.

Find the differential equation of a family of curves given by y = a cos (mx + b), a and b being arbitrary constants.

Form the differential equation for the following:
a) y = mx
\(b) \ \mathbf{y}=m x+\frac{a}{m} , \) (m is arbitrary constant)
\(c) \ y=a \cos 3 x+b \sin 3 x \)
\(d) \ x^{2}+y^{2}=a^{2} \)