Exercise
$\frac{dy}{dx}-\cos\left(x\right)=5y$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx-cos(x)=5y. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -\cos\left(x\right) from both sides of the equation. Multiply -1 times -1. Rearrange the differential equation. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=-5 and Q(x)=\cos\left(x\right). In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation dy/dx-cos(x)=5y
Final answer to the exercise
$y=\frac{-5\cos\left(x\right)+\sin\left(x\right)}{24}$