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

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 differential equation of system of concentric circles with centre (1,2).

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)

Find the equation of a curve passing through the point (1, 1), if the tangent drawn at any point P(x, y) on the curve meets the coordinate axes at A and B such that P is the mid-point of AB.

4

(a)