Final answer to the problem
$y=\sqrt{2\left(-e^x\cdot x+e^x+C_0\right)},\:y=-\sqrt{2\left(-e^x\cdot x+e^x+C_0\right)}$
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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
Learn how to solve integration techniques problems step by step online.
$ye^{-x}dy=1-x\cdot dx$
Learn how to solve integration techniques problems step by step online. Solve the differential equation xdx+ye^(-x)dy=1. Grouping the terms of the differential equation. 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{-x}{e^{-x}}dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Final answer to the problem
$y=\sqrt{2\left(-e^x\cdot x+e^x+C_0\right)},\:y=-\sqrt{2\left(-e^x\cdot x+e^x+C_0\right)}$
