Final answer to the problem
$\frac{-3-4y}{8e^{4y}}=\frac{\sin\left(2x\right)+\cos\left(2x\right)}{4e^{2x}}$
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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
Factoring by $e^{\left(2x-3y\right)}$
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$e^y\sin\left(2x\right)\cdot dx+e^{\left(2x-3y\right)}\left(1+2y\right)dy=0$
Learn how to solve problems step by step online. Solve the differential equation e^ysin(2x)dx+(e^(2x-3y)+2ye^(2x-3y))dy=0. Factoring by e^{\left(2x-3y\right)}. Grouping the terms of the differential equation. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality.
Final answer to the problem
$\frac{-3-4y}{8e^{4y}}=\frac{\sin\left(2x\right)+\cos\left(2x\right)}{4e^{2x}}$
