# Find the general solution of the differential equation $$\frac{dy}{dx}=3e^x+2$$

Category: QuestionsFind the general solution of the differential equation $$\frac{dy}{dx}=3e^x+2$$
Editor">Editor Staff asked 11 months ago

Find the general solution of the differential equation $$\frac{dy}{dx}=3e^x+2$$

(a) y=3e^x+2x+C

(b) y=3e^x-2x+C

(c) y=2e^x+3x+C

(d) y=2e^x-3x+C

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Asked question is from Methods of Solving First Order & First Degree Differential Equations topic in section Differential Equations of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

Right choice is (a) y=3e^x+2x+C

For explanation: Given that, $$\frac{dy}{dx}=3e^x+2$$

Separating the variables, we get

dy=(3e^x+2)dx

Integrating both sides, we get

$$\int dy=\int (3e^x+2)\,dx$$ –(1)

y=3e^x+2x+C which is the general solution of the given differential equation.