Exercise
$\frac{dy}{dx}+y\cot\left(x\right)=-y^2\sin^2\left(x\right)$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx+ycot(x)=-y^2sin(x)^2. We identify that the differential equation \frac{dy}{dx}+y\cot\left(x\right)=-y^2\sin\left(x\right)^2 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 2. Simplify. Isolate the dependent variable y.
Solve the differential equation dy/dx+ycot(x)=-y^2sin(x)^2
Final answer to the exercise
$y=\frac{\csc\left(x\right)}{\cos\left(x\right)+C_0}$