1. The problem statement, all variables and given/known data dx/dt= -x2-2x(1+t+t2) x(1)=2 estimate x(1.2) with h=0.2 2. Relevant equations Implicit Euler: I was taught that we must solve for yk+1 using Newton's method: This doesn't seem like it will work because newton's method assumes a function of only one variable. According to wikipedia though: The backward Euler method is an implicit method: the new approximation appears on both sides of the equation, and thus the method needs to solve an algebraic equation for the unknown [PLAIN]http://upload.wikimedia.org/math/6/6/7/6675fbec7c9571df0f0c413acd3fcab8.png. [Broken] 3. The attempt at a solution dx/dt= -x2-2x(1+t+t2) let x(1)=2 be denoted by x0, x(1.2) is denoted by x1 using implicit euler formula: x1=2+0.2[-x12-2x1(1+1.2+1.22)] 0=2-0.2x12-2.456x1 ==> proceed with quadratic formula to solve for x1 My question is whether this method is valid to solve for x1? Edit: it appears that it is possible to solve for x1 using multivariable newton's method. This would require finding the inverse matrix of the Jacobian of F.