Exercise
$y'=x^3\left(x^2+5\right)\left(x-1\right)^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'=x^3(x^2+5)(x-1)^2. Rewrite the differential equation using Leibniz notation. 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^3\left(x^2+5\right)\left(x-1\right)^2dx. 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 y^'=x^3(x^2+5)(x-1)^2
Final answer to the exercise
$y=\frac{x^{8}}{8}+\frac{-2x^{7}}{7}+x^{6}-2x^{5}+\frac{5x^{4}}{4}+C_0$