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Divide all the terms of the differential equation by $\cos\left(x\right)^2\sin\left(x\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{dy}{dx}\frac{\cos\left(x\right)^2\sin\left(x\right)}{\cos\left(x\right)^2\sin\left(x\right)}+\frac{y\cos\left(x\right)^3}{\cos\left(x\right)^2\sin\left(x\right)}=\frac{1}{\cos\left(x\right)^2\sin\left(x\right)}$
Learn how to solve differential calculus problems step by step online. Solve the differential equation cos(x)^2sin(x)dy/dx+cos(x)^3y=1. Divide all the terms of the differential equation by \cos\left(x\right)^2\sin\left(x\right). 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{\cos\left(x\right)}{\sin\left(x\right)} and Q(x)=\frac{1}{\cos\left(x\right)^2\sin\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.