Differential Equations - dy/dx = f(x)
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Differential equations of the form are very common and easy to solve. The following shows how to do it:
Step 1
First we multiply both sides by to obtain
Step 2
Then we take the integral of both sides to obtain
where is the integral constant of We can neglect since another integral constant is hidden in the integral
Therefore, we can conclude that if then
Find in terms of where
We have
Find in terms of where and
We have
Substituting gives
and therefore our answer is
References
Editorial: PHH Ecuaciones diferenciales elementales y problemas con condiciones en la frontera authors: C.H Edwards, David Penney