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- Exact Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
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- FOIL Method
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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
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$6y^2dy=x\left(e^{\left(x^2\right)}+2\right)dx$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(x(e^x^2+2))/(6y^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.
