Final answer to the problem
$\frac{\sqrt{\pi }\mathrm{erf}\left(y\right)}{2}=\frac{e^x}{-2x^{2}}+\frac{e^x}{-2x}+\frac{1}{2}Ei\left(x\right)+C_0$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Rewrite the differential equation using Leibniz notation
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$x^3\frac{dy}{dx}=e^{\left(x+y^2\right)}$
Learn how to solve problems step by step online. Solve the differential equation x^3y^'=e^(x+y^2). Rewrite the differential equation using Leibniz notation. Rewrite the differential equation. 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.
Final answer to the problem
$\frac{\sqrt{\pi }\mathrm{erf}\left(y\right)}{2}=\frac{e^x}{-2x^{2}}+\frac{e^x}{-2x}+\frac{1}{2}Ei\left(x\right)+C_0$
