Differential Equations Question 7
Question: The solution of the equation $ \sqrt{a+x}\frac{dy}{dx}+x=0 $ is
[DSSE 1988]
Options:
A) $ 3y+2\sqrt{a+x}.(x-2a)=3c $
B) $ 3y+2\sqrt{x+a}.(x+2a)=3c $
C) $ 3y+\sqrt{x+a}.(x+2a)=3c $
D) None of these
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Answer:
Correct Answer: A
Solution:
$ \sqrt{a+x}\frac{dy}{dx}+x=0 $
Therefore $ \int _{{}}^{{}}{dy}=-\int _{{}}^{{}}{\frac{x}{\sqrt{a+x}}dx} $
Therefore $ y=-\int _{{}}^{{}}{\sqrt{a+x}}dx+\int _{{}}^{{}}{\frac{a}{\sqrt{a+x}}}dx $
$ { \because \int _{{}}^{{}}{\frac{x}{\sqrt{a+x}}}dx=\int _{{}}^{{}}{\frac{x+a-a}{\sqrt{a+x}}}dx } $
Therefore $ y=-\frac{2}{3}{{(a+x)}^{3/2}}+2a\sqrt{a+x}+c $
Therefore $ 3y=-\sqrt{a+x}(2(a+x)-6a)+3c $
Therefore $ 3y=-2\sqrt{a+x}(x-2a)+3c $
Therefore $ 3y+2\sqrt{a+x}(x-2a)=3c $ .
BETA
