The differential equation of the family of curves y = Ae^x + Be^−x, where A and B are arbitrary constants is

The solution of the differential equation \(2x\frac{dy}{dx}-y=3\) represents

The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

The solution of (x² - ay)dx = (ax - y²)dy is ___________

The transformation y = vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \) __________ 

For each of the following differential equations, determine its order, degree (if exists)
\(\sqrt { \frac { dy }{ dx } } -4\frac { dy }{ dx } -7x=0\)

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

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

Solve: x \(\frac{dy}{dx}=x+y\)

Solve: \(\frac{dy}{dx}+y=e^{-x}\)

Determine the order and degree (if exists) of the following differential equations: 
dy + (xy − cos x)dx = 0

Show that y = 2(x²−1)+Ce^−x2 is a solution of the differential equation \(\frac { dy }{ dx } +2xy-4{ x }^{ 3 }=0\)

Solve \((1+{ 2e }^{ x/y })dx+2{ e }^{ x/y }\left( 1-\frac { x }{ y } \right) dy=0\)

Form the differential equation for y = e^-2x [A cos 3x-B sin 3x]

Solve: \(\frac{dy}{dx}+y=cos x\)

Solve y' = sin² (x − y + 1 ).

Solve:\(\frac { dy }{ dx } \) = (3x+y+4)².