Solve each of the following initial value problems ,y(1) = 0 A differential equation is shown: dy/dx - y/x + cosec(y/x) = 0.

Q36 of 462 Page 23

Solve each of the following initial value problems
,y(1) = 0

,y(1) = 0

It is a homogeneous equation

Put y = vx

And

So,

Integrating both sides we get,

– cos v = – log x + c

put value of v,

– cos = – log x + c …… (1)

Put y = 0, x = 1,We have

c = – 1

Now,

– cos = – log x – 1

log x = cos – 1

Solve each of the following initial value problems

(x² + y²)d x = 2xy dy, y(1) = 0

Solve each of the following initial value problems

,y(e) = 0

Solve each of the following initial value problems

(xy–y²)dx+x²dy=0,y(1) = 1

Solve each of the following initial value problems

,y(1) = 2