![]() Put another way: how Mathematica does things doesn't necessarily correspond to 'manual' methods. So, it is no wonder that a brute force solution using Solve on the original equations takes forever. A typical problem is that Mathematica has many internal optimizations, and the efficiency of a computation can be greatly affected by whether the details of the computation do or do not allow a given internal optimization to be used. However, the subsequent expressions are likely to be equally enormous. NDSolve can also solve some differential-algebraic equations, which are typically a mix of differential and algebraic equations. ![]() It can handle a wide range of ordinary differential equations as well as some partial differential equations. In principle one could back-substitute the h3 solutions into the preceding equation and solve for h2, etc. The Mathematica function NDSolve is a general numerical differential equation solver. The size of the answers first grows and then shrinks, as shown at the end. h_] did not return an answer in a reasonable amount of time, so I begin eliminating variables one at a time, which is quite fast. Is there any way to get an exact solution a system of non-linear equations?
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