Final answer to the problem
$e^{\frac{1}{200}x^2}y=42\sum_{n=0}^{\infty } \frac{\left(\frac{1}{200}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
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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
Expand the fraction $\frac{4200-yx}{100}$ into $2$ simpler fractions with common denominator $100$
$\frac{dy}{dx}=\frac{4200}{100}+\frac{-yx}{100}$
Learn how to solve integrals of polynomial functions problems step by step online.
$\frac{dy}{dx}=\frac{4200}{100}+\frac{-yx}{100}$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dy/dx=(4200-yx)/100. Expand the fraction \frac{4200-yx}{100} into 2 simpler fractions with common denominator 100. Divide 4200 by 100. Rearrange the differential equation. Simplifying.
Final answer to the problem
$e^{\frac{1}{200}x^2}y=42\sum_{n=0}^{\infty } \frac{\left(\frac{1}{200}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
