Question

solve the following differential equation-

x (dy/dx)= y+x+(x tan(y/x)), given t=pi/2 when x=1

Answer 1

Answer:

The given equation is an exact differential equation. It is

re-written as xdy+ydx=xlogx or d(xy)=xlogxintegration by parts method used

Its solution is

xy=Integral of (x.logx .dx=(1/2. x^2)logx-x/2 +c where c is an arbitrary constant (