Exercise
$x\left(y'-5y\right)=10x^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation x(y^'-5y)=10x^2. Rewrite the differential equation using Leibniz notation. Divide both sides of the equation by x. Simplify the fraction \frac{10x^2}{x} by x. 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)=10x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation x(y^'-5y)=10x^2
Final answer to the exercise
$y=\left(\frac{-10x-2}{5e^{5x}}+C_0\right)e^{5x}$