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

Solve: x \(\frac{dy}{dx}=x+y\)

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

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

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