Ordinary Differential Equations
Not what you're looking for? Search our solutions OR ask your own Custom question.
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.
© BrainMass Inc. brainmass.com December 24, 2021, 6:24 pm ad1c9bdddfhttps://brainmass.com/math/ordinary-differential-equations/solving-ordinary-differential-equations-111271
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
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.
$2.49