Final answer to the problem
$y=\frac{e^{3x^2}}{-4\sum_{n=0}^{\infty } \frac{3^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0}$
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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
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1
Grouping the terms of the differential equation
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$\frac{dy}{dx}-4y^2=6xy$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=4y^2+6xy. Grouping the terms of the differential equation. Rearrange terms. We identify that the differential equation \frac{dy}{dx}-6xy=4y^2 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 2.
Final answer to the problem
$y=\frac{e^{3x^2}}{-4\sum_{n=0}^{\infty } \frac{3^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0}$
