Exercise
$\left(100+2x\right)y'+y=7\left(100+2x\right)$
Step-by-step Solution
Learn how to solve trigonometric integrals problems step by step online. Solve the differential equation (100+2x)y^'+y=7(100+2x). Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by 100+2x. 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{1}{100+2x} and Q(x)=7. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation (100+2x)y^'+y=7(100+2x)
Final answer to the exercise
$y=\frac{7\sqrt{\left(100+2x\right)^{3}}+C_1}{3\sqrt{100+2x}}$