Solve the differential equation: y+ \(\frac {d}{dx}\)(xy) = s (sin x + log x)

4

(a)

Solve the differential equation: (x + y) (dx - dy) = dx + dy

4

(a)

If y(t) is a solution of (1 + t) \(\frac{dy}{dt}\) - ty = 1 and y(0) = -1, then show that y(1) = -\(\frac {1}{2}\)

4

(a)

Find the general solution of the following differential equations :
\(\left( 1+{ y }^{ 2 } \right) +\left( x-{ e }^{ \tan ^{ -1 }{ y } } \right) \frac { dy }{ dx } =0\)

4

(a)

Find the equation of a curve whose tangent at any point on it, different from origin, has slope \(y+\frac{y}{x}\).

4

(a)