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
Correct Answer: A
Solution :
\[\sqrt{a+x}\frac{dy}{dx}+x=0\] Þ \[\int_{{}}^{{}}{dy}=-\int_{{}}^{{}}{\frac{x}{\sqrt{a+x}}dx}\] Þ \[y=-\int_{{}}^{{}}{\sqrt{a+x}}dx+\int_{{}}^{{}}{\frac{a}{\sqrt{a+x}}}dx\] \[\left\{ \because \int_{{}}^{{}}{\frac{x}{\sqrt{a+x}}}dx=\int_{{}}^{{}}{\frac{x+a-a}{\sqrt{a+x}}}dx \right\}\] Þ \[y=-\frac{2}{3}{{(a+x)}^{3/2}}+2a\sqrt{a+x}+c\] Þ \[3y=-\sqrt{a+x}(2(a+x)-6a)+3c\] Þ \[3y=-2\sqrt{a+x}(x-2a)+3c\] Þ \[3y+2\sqrt{a+x}(x-2a)=3c\].
You need to login to perform this action.
You will be redirected in
3 sec
