Solve each of the following initial value problems ,y(e) = 0 The image displays the differential equation x e^(y/x) - y + x dy/dx = 0.

Q36 of 462 Page 23

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

,y(e) = 0

It is a homogeneous equation

Put y = vx

And

So,

On integrating both sides,

log xc

v = log(log xc)

put value of v,

log(log x) + k ……(1)

Put y = 0, x = e

0 = e log(log e) + k

k = 0

put in eq. (1),

y = x log(log(x))

Solve the following differential equations :

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(1) = 0

Solve each of the following initial value problems

(xy–y²)dx+x²dy=0,y(1) = 1