# Ordinary Differential Equations

Explain how to solve differential equations of the following types:

y'=f(ax+by+c)

y'=f(y/x)

x=f(y,y')

Provide examples with complete solutions for each case.

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I. The method. Let with f a continuous function. There is a simple trick to solve this type of differential equation: let us introduce the auxiliary function

(recall that y is a function of x). Then:

and So, by simple substitution, we get:

which is very easy to solve!

Example: to solve we put u=x+y+3, so we have to solve:

because a=b=1 in this case. The ...

#### Solution Summary

Ordinary differential equations are solved. The solution is detailed and well presented. Examples with completed solutions for each case are determined.

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