Exercise
$\frac{dy}{dx}=x^2e^{x^3-y}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=x^2e^(x^3-y). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. 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}{e^{-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 differential equation dy/dx=x^2e^(x^3-y)
Final answer to the exercise
$y=\ln\left(\frac{e^{\left(x^3\right)}+C_1}{3}\right)$