Final answer to the problem
$y=\sqrt{2\left(2e^x-x+C_0\right)},\:y=-\sqrt{2\left(2e^x-x+C_0\right)}$
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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
Group the terms of the equation
$-y\cdot dy=-2e^xdx+dx$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation -ydy+2e^xdx-dx=0. Group the terms of the equation. Multiply both sides of the equation by -1. Factor the polynomial 2e^xdx-dx by it's greatest common factor (GCF): 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
$y=\sqrt{2\left(2e^x-x+C_0\right)},\:y=-\sqrt{2\left(2e^x-x+C_0\right)}$
