I have difficulties with this equation$$\frac{d^2 u}{d x^2} + u^2 - x^2 = 0$$with boundary conditions: $u(0)=u(1)=0$I do not know how to solve nonlinear differential equations with Newton's method. If somebody knows could you please explain? I followed the comments and  finally reach these two equations (eqn1 and eqn2). But my problem is that from now on ,   do not have any idea to combine these two equations. f somebody has any idea,  will be thankful so much for sharing with me. I just applied the newton raphson method
Solving nonlinear differential equations with Newton's method
numerical analysis;nonlinear equations