Final answer to the problem
$y=\left(-2\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)e^{\frac{1}{2}x^2}$
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Step-by-step Solution
How should I solve this problem?
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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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$xy-2y+x-2-\frac{dy}{dx}=0$
Learn how to solve problems step by step online. Solve the differential equation xy-2yx+-2-y^'=0. Rewrite the differential equation using Leibniz notation. Multiplying the fraction by -1. Eliminate the minus (-) sign from the differential by multiplying the whole differential equation by -1. Grouping the terms of the differential equation.
Final answer to the problem
$y=\left(-2\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)e^{\frac{1}{2}x^2}$
