Exercise
$\frac{dy}{dx}=x\left(e^{x^2}+2\right)$
Step-by-step Solution
Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dx=x(e^x^2+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 x\left(e^{\left(x^2\right)}+2\right)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(e^{\left(x^2\right)}x+2x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Solve the differential equation dy/dx=x(e^x^2+2)
Final answer to the exercise
$y=\frac{1}{2}e^{\left(x^2\right)}+x^2+C_0$