Final answer to the problem
$\ln\left|y\right|=e^{\left(x+2\right)}x-e^{\left(x+2\right)}-x+C_0$
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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
Grouping the terms of the differential equation
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$\frac{dy}{dx}=yxe^{\left(x+2\right)}-y$
Learn how to solve problems step by step online. Solve the differential equation dy/dx+y=yxe^(x+2). 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. Factor the polynomial e^2yxe^x-y by it's greatest common factor (GCF): y. 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
$\ln\left|y\right|=e^{\left(x+2\right)}x-e^{\left(x+2\right)}-x+C_0$
