Ordinary Differential Equations
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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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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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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 ...
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