Question

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

This question was posed to me in my homework.

Asked question is from Methods of Solving First Order & First Degree Differential Equations topic in section Differential Equations of Mathematics – Class 12

Answer 1

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.