Differential-Equations Question 387
Question: The solution of $ {e^{dy/dx}}=(x+1) $ , $ y(0)=3 $ is
[Kerala (Engg.) 2005]
Options:
A) $ y=x\log x-x+2 $
B) $ y=(x+1)\log |x+1|-x+3 $
C) $ y=(x+1)\log |x+1|+x+3 $
D) $ y=x\log x+x+3 $
E) $ y=-(x+1)\log |x+1|+x+3 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{dy}{dx}=\log (x+1) $
Þ $ dy=\log (x+1)dx $ $ y=\int{\log (x+1)dx}=x.\log (x+1)-\int{\frac{x}{x+1}dx} $ $ =x.\log (x+1)-\int{( 1-\frac{1}{x+1} )},dx $ $ =x.\log (x+1)-x+\log (x+1)+c=(x+1)\log (x+1)-x+c $ $ x=0 $ at $ y=3 $ $ 3=(1)\log (1)-0+c $
Þ $ 3=0+c $
Þ $ c=3 $ \ $ y=(x+1)\log |x+1|-x+3 $ .
BETA
