Final answer to the problem
$e^{\left(-y^2-y\right)}=\frac{1}{2}\left(e^x\sin\left(x\right)-e^x\cos\left(x\right)\right)$
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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
Grouping the terms of the differential equation
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$\left(2y+1\right)e^{-y^2}dy=-e^{\left(x+y\right)}\sin\left(x\right)dx$
Learn how to solve problems step by step online. Solve the differential equation e^(x+y)sin(x)dx+(2y+1)e^(-y^2)dy=0. 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. Simplify the expression \frac{e^{-y^2}\left(2y+1\right)}{e^y}dy.
Final answer to the problem
$e^{\left(-y^2-y\right)}=\frac{1}{2}\left(e^x\sin\left(x\right)-e^x\cos\left(x\right)\right)$
