Final Answer
Step-by-step Solution
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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
Learn how to solve differential equations problems step by step online.
$dy=\left(x+1\right)^2dx$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(x+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 \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. Expand the integral \int\left(x^2+2x+1\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.