All Differential Equations Resources
Example Questions
Example Question #11 : Initial Value Problems
Solve the following initial value problem: ,
.
Possible Answers:
Correct answer:
Explanation:
This type of problem will require an integrating factor. First, let's get it into a better form: . Once we have an equation in the form
, we find
(where the constant of integration is omitted because we only need one, arbitrary integrating factor).
Once we do this, we can see that
This is simply due to product rule, and then at the end, substitution of the original equation. Thus, as we know that , we can just integrate both sides to find y.
. A quick application of integration by parts with
and
tells us that the right hand side is
. Dividing both sides by mu, we are left with
. Plugging in the initial condition, we find
giving us
. Thus, we have a final answer of
.
Philip
Certified Tutor
Certified Tutor
Texas Tech University, Doctor of Philosophy, Higher Education Administration.
Robert
Certified Tutor
Certified Tutor
Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.
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