Final answer to the problem
$\frac{e^{\frac{15}{2}x^2}}{y^{5}}=5\sum_{n=0}^{\infty } \frac{\left(\frac{15}{2}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
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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
Multiplying polynomials $y$ and $3x-y^5$
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$\frac{dy}{dx}=3yx-yy^5$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=y(3x-y^5). Multiplying polynomials y and 3x-y^5. When multiplying exponents with same base you can add the exponents: -yy^5. Grouping the terms of the differential equation. Rearrange terms.
Final answer to the problem
$\frac{e^{\frac{15}{2}x^2}}{y^{5}}=5\sum_{n=0}^{\infty } \frac{\left(\frac{15}{2}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
