For each of the following differential equations, determine its order, degree (if exists)
\(\frac { dy }{ dx } +xy=cotx\)

For each of the following differential equations, determine its order, degree (if exists)
\({ \left( \frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } \right) }^{ \frac { 2 }{ 3 } }-3\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +5\frac { dy }{ dx } +4=0\)

For each of the following differential equations, determine its order, degree (if exists)
\({ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0\)

For each of the following differential equations, determine its order, degree (if exists)
\({ \left( \frac { d^2y }{ dx^2 } \right) }^{ 3 }=\sqrt { 1+\left( \frac { dy }{ dx } \right) } \)

Find the differential equation corresponding to the family of curves represented by the equation y = Ae^8x + Be^-8x, where A and B are arbitrary constants.

Find value of m so that the function y = e^mx is a solution of the given differential equation.
y '+ 2y = 0

Determine the order and degree (if exists) of the following differential equations: 
\({ \left( \frac { { d }^{ 4 }y }{ { dx }^{ 4 } } \right) }^{ 3 }+4{ \left( \frac { dy }{ dx } \right) }^{ 7 }+6y=5cos3x\)

Find the differential equation of the family of parabolas y² = 4ax, where a is an arbitrary constant.

Show that y = mx + \(\frac{7}{m}\), m ≠ 0 is a solution of the differential equation xy'+7\(\frac{1}{y'}\)-y = 0.

Solve the Linear differential equation:
\(\frac { dy }{ dx } =\frac { { sin }^{ 2 }x }{ 1+{ x }^{ 3 } } -\frac { { 3x }^{ 2 } }{ 1+{ x }^{ 3 } } y\)

Form the differential equation satisfied by are the straight lines in my-plane.

A curve passing through the origin has its slope e^x, Find the equation of the curve.

Solve: \(\frac{dy}{dx}=1+e^{x-y}\)

Solve: x \(\frac{dy}{dx}=x+y\)

Solve: \(\frac{dy}{dx}+y=e^{-x}\)