Question

Solve the initial-value problem:
x*(dy/dx)-y/(x+1)=x, y(1)=0, x>0
Please show your work! I'm confused.

Answer 1

\[xy'-\frac{1}{x+1}y=x\\
y'-\frac{1}{x(x+1)}y=1\]
Linear ODE, so find the integrating factor:
\[\mu(x)={\large e}^{\displaystyle\int\frac{dx}{x(x+1)}}\]

Answer 2

Thanks~!

Answer 3

yw