Final answer to the problem
$y=\frac{1}{e^{\frac{x^2}{2}}\left(-\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)}$
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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
Learn how to solve integrals of polynomial functions problems step by step online.
$y^2+xy+\frac{dy}{dx}=0$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation y^2+xyy^'=0. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting y^2+xy from both sides of the equation. Solve the product -\left(y^2+xy\right). Grouping the terms of the differential equation.
Final answer to the problem
$y=\frac{1}{e^{\frac{x^2}{2}}\left(-\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)}$
