The integrating factor method is used when the differential equation is (or can be rearranged) in the form
where p and q are functions of x only.
How do we find the integrating factor?
The integrating factor is .
How do we solve differential equations using this method?
Rearrange the differential equation (if needed) to the standard form and find the integrating factor. Multiply through by the integrating factor and rewrite the left hand side with derivatives y. Integrate both sides gives the general solution.
Solve with y(0) = 1.
Step1:Compare the equation with the standard form
gives and .
Step2:Find the integrating factor
Step3:Multiply through by the integrating factor, we get .
Step4:Replace with derivative of i.e. .
Step5:Integrate both sides and get .
Step6:Use the initial condition to find c. , gives . Hence the solution to the problem is which is