Solve the differential equation:\(\frac { dy }{ dx } +1={ e }^{ x+y }\)

Solve the differential equation: y - x \(\frac { dy }{ dx } =a\left( { y }^{ 2 }+{ x }^{ 2 }\frac { dy }{ dx } \right) ,\) where x = a, y = a.

Solve the differential equation: sec² y (1+x²) dy 2x tan y dx = 0, given that \(y=\frac {\pi}{4}\), when x = 1.

Solve the differential equation: \(\frac {dy}{dx}\) + y cot x = 2 cos x .

Solve the differential equation: \(\frac {dy}{dx} = tan (x + y)\)

Solve the differential equation: log \((\frac {dy}{dx}) = ax + by\)

Solve the differential equation: (1+y²⁾ dx - y (1+x²) dy = 0, given that y = 0, when x =1.

Show that the function y = Ax + \(\frac {B}{x}\) is a solution of the differential equation x² \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +x\frac { dy }{ dx } -y=0.\)

Find the differential equation of all circles which pass through orgin and whose centre lies on the y-axis.

Form the differential equation corresponding to y² = a(b - x)(b + x) by eliminating a and b are arbitary constants.

Obtain the differential equation of all the circles of radius r.

Find the particular solution of the differential equation (tan^-1 y - x) dy = (1 + y²) dx, given that when x = 0, y = 0.

Find the particular solution of the differential equation (x - siny) dy + (tany) dx = 0, given that y = 0 when x = 0.

Find the particular solution of the differential equation \(\frac { dy }{ dx } =\frac { xy }{ { x }^{ 2 }+{ y }^{ 2 } } \) given that y = 1, when x = 0.

Find the particular solution satisfying the given condition : \({ x }^{ 2 }dy+\left( xy+{ y }^{ 2 } \right) dx=0\); y = 1, when x = 1.

Find the particular solution of the differential equation :
\(x{ e }^{ \frac { y }{ x } }-y\sin { \left( \frac { y }{ x } \right) } +x\frac { dy }{ dx } \sin { \left( \frac { y }{ x } \right) } =0\) for x = 1, y = 0.

Find the particular solution of the following differential equation given that : y = 0, when x = 1 : (x² + xy) dy = (x² + y²) dx.

Find the particular solution of the differential equation : x²dy = y(x + y)dx = 0, when x = 1, y = 1.

Find the particular solution of the differential equation
\(xcos\left( \frac { y }{ x } \right) \frac { dy }{ dx } =ycos\left( \frac { y }{ x } \right) +x\) given that when x = 1, y = \(\frac { \pi }{ 4 } \)

Solve the following differential equation:
\(xcos\left( \frac { y }{ x } \right) (ydx+xdy)=ysin\left( \frac { y }{ x } \right) (xdy-ydx)\)