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
 
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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
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.