Exercise
$\frac{dy}{dx}=\frac{9+11x}{xy^2},\:y\left(1\right)=2$
Step-by-step Solution
Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dx=(9+11x)/(xy^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 \left(9+11x\right)\frac{1}{x}dx. 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 y^2dy and replace the result in the differential equation.
Solve the differential equation dy/dx=(9+11x)/(xy^2)
Final answer to the exercise
$y=\sqrt[3]{3}\sqrt[3]{9\ln\left(x\right)+11x-\frac{25}{3}}$