Exercise
$x^2\frac{dy}{dx}-2xy=x^4\cos\left(x\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation x^2dy/dx-2xy=x^4cos(x). Divide all the terms of the differential equation by x^2. Simplifying. 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)=\frac{-2}{x} and Q(x)=x^{2}\cos\left(x\right). In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
Solve the differential equation x^2dy/dx-2xy=x^4cos(x)
Final answer to the exercise
$y=x^{2}\left(\sin\left(x\right)+C_0\right)$