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: \(\frac{dy}{dx}+y=e^{-x}\)

Determine the order and degree of \(\frac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 3 }{ 2 } } }{ \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =k\)

Find the order and degree of \(\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+cos\left( \frac { dy }{ dx } \right) =0\)

Find the order and degree of \(y+\frac { dy }{ dx } =\frac { 1 }{ 4 } \int { ydx } \)

Form the Differential Equation representing the family of curves y = A cos(x + B) where A and B are parameters.

Form the D.E of family of parabolas having vertex at the origin and axis along positive y-axis.

Form the D.E corresponding to y=e^mx by eliminating 'm'.

Solve :\(\frac { dy }{ dx } =\frac { 2x }{ { x }^{ 2 }+1 } \)

Solve : \(\frac { dy }{ dx } =\frac { { e }^{ x }-{ e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } \)

Solve:\(\frac { dy }{ dx } +y=1\)

solve: x dy + y dx = xy dx