Math Is Fun Forum

EPhillips1989

Member

Registered: 2007-11-03

Posts: 29

general solution for a differential equation

can anyone please help me solve the following differential equation
x(dy/dx)-y=xtan(y/x)

so far i have done

x^2(dy/dx)-yx=x^2tan(y)
looking for a solution of the LHS=0
x^2(dy/dx)-yx=0
seeking a solution of the full equation in the form y=xv(x)
dy/dx=v+x(dv/dx)

substitute in full equation

x^2(v+x(dv/dx))-xv*x=x^2tan(vx)

x^2v+x^3(dv/dx)-x^2v=x^2tan(vx)
x^3(dv/dx)=x^2tan(vx)
x(dv/dx)=tan(xv)

and then i cant go any further please help!!!!!!!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: general solution for a differential equation

This is a homogeneous linear differential equation. Use the substitution y = ux.

EPhillips1989

Member

Registered: 2007-11-03

Posts: 29

Re: general solution for a differential equation

yes thats what ive done with a substitution of y=vx

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: general solution for a differential equation

Now that’s easy to solve.