Final answer to the problem
$y=\frac{\ln\left(\frac{3}{-2\left(e^{3x}+C_1\right)}\right)}{2}$
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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 using Leibniz notation
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$\frac{dy}{dx}=e^{\left(3x+2y\right)}$
Learn how to solve problems step by step online. Solve the differential equation y^'=e^(3x+2y). Rewrite the differential equation using Leibniz notation. 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. 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
$y=\frac{\ln\left(\frac{3}{-2\left(e^{3x}+C_1\right)}\right)}{2}$
