Question

DIFFERENTIAL CALCULUS

dx/dy=8-3x; x(0)=2

Answer 1

dx/(8-3x)=dy.

Integrate both sides:

-⅓ln|8-3x|=y+C.

When y=0, x=2:

-⅓ln(2)=C,

ln|2/(8-3x)|=y³,

2/(8-3x)=e^y³,

8-3x=2e^(-y³),

3x=8-2e^(-y³), x=⅔(4-e^(-y³)).