Differential Equations Question 251
Question: Solution of differential equation $ \frac{dy}{dx}+ay=e^{mx} $ is
[MP PET 1996]
Options:
A) $ (a+m)y=e^{mx}+c $
B) $ ye^{ax}=me^{mx}+c $
C) $ y=e^{mx}+c{e^{-ax}} $
D) $ (a+m)y=e^{mx}+c{e^{-ax}}(a+m) $
Show Answer
Answer:
Correct Answer: D
Solution:
I.F. $ ={e^{\int _{{}}^{{}}{adx}}}=e^{ax} $
$ \therefore $ Required solution is given by $ y.e^{ax}=\int _{{}}^{{}}{e^{mx}.e^{ax}}dx=\frac{{e^{(a+m)x}}}{a+m}+C $
Therefore $ y=\frac{e^{mx}}{a+m}+C{e^{-ax}} $
Therefore $ y(a+m)=e^{mx}+C(a+m){e^{-ax}} $ .
BETA
