Exercise
$\frac{dy}{dx}=y^{2\:}sinx;\:y\left(\pi\right)=-\frac{1}{2}$
Step-by-step Solution
Learn how to solve limits to infinity problems step by step online. Solve the differential equation dy/dx=y^2sin(x),ypi=-1/2. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{y^2}\frac{1}{\pi y}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{\pi y^{3}}dy and replace the result in the differential equation.
Solve the differential equation dy/dx=y^2sin(x),ypi=-1/2
Final answer to the exercise
$y=\frac{1}{\sqrt{\pi \left(-\cos\left(x\right)+C_2\right)}},\:y=\frac{-1}{\sqrt{\pi \left(-\cos\left(x\right)+C_3\right)}}$