Final answer to the problem
$y=\sqrt{\ln\left(e^{2x}+C_1\right)},\:y=-\sqrt{\ln\left(e^{2x}+C_1\right)}$
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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
Rewrite the differential equation
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$\frac{dy}{dx}=\frac{e^{\left(2x-y^2\right)}}{y}$
Learn how to solve problems step by step online. Solve the differential equation ydy/dx=e^(2x-y^2). Rewrite 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{y}{e^{-y^2}}dy.
Final answer to the problem
$y=\sqrt{\ln\left(e^{2x}+C_1\right)},\:y=-\sqrt{\ln\left(e^{2x}+C_1\right)}$
