Step-by-step Solution

Solve the differential equation $\frac{dy}{dx}=e^{\left(3x+2y\right)}$

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Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=e^{3x+2y}$

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}=e^{3x}e^{2y}$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=e^(3x+2y). 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{e^{2y}}dy and replace the result in the differential equation.

Final Answer

$y=\frac{\ln\left(\frac{-\frac{1}{2}}{\frac{1}{3}e^{3x}+C_0}\right)}{2}$