Final answer to the problem
$y=\frac{\ln\left(3\left(\frac{-1}{8e^{2x}}+C_0\right)\right)}{3}$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
$\frac{dy}{dx}=\frac{e^{\left(-2x-3y\right)}}{4}$
Learn how to solve rational equations problems step by step online.
$\frac{dy}{dx}=\frac{e^{\left(-2x-3y\right)}}{4}$
Learn how to solve rational equations problems step by step online. Solve the differential equation 4dy/dx=e^(-2x-3y). 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{1}{e^{-3y}}dy.
Final answer to the problem
$y=\frac{\ln\left(3\left(\frac{-1}{8e^{2x}}+C_0\right)\right)}{3}$
