Final answer to the problem
$y=\left(\frac{\sqrt{\pi }\mathrm{erf}\left(x\right)}{2}+C_0\right)e^{\left(x^2\right)}$
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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
Divide both sides of the equation by $dx$
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$1+2xy=\left(1+y^2\right)\frac{dy}{dx}$
Learn how to solve problems step by step online. Solve the differential equation (1+2xy)dx=(1+y^2)dy. Divide both sides of the equation by dx. Group the terms of the equation. Multiplying the fraction by -\left(1+y^2\right). Eliminate the minus (-) sign from the differential by multiplying the whole differential equation by -1.
Final answer to the problem
$y=\left(\frac{\sqrt{\pi }\mathrm{erf}\left(x\right)}{2}+C_0\right)e^{\left(x^2\right)}$
