Question

Using the substitution v=y/x, solve the IVP

y*y' = x^3 + (y^2)/x; y(2) = 6

Answer 1

whats y*

Answer 2

y multiplied by y prime

i.e. y * dy/dx

Answer 3

y(y' - y/x ) = x^3
y=vx
y' = v + xdv/dx

so
vx(v + xdv/dx -v) = x^3
vx^2dv/dx = x^3
vdv/dx= x
vdv=xdx
v^2 = x^2 +c

Answer 4

there you go..