A) -1
B) 2
C) 1
D) 0
Correct Answer: D
Solution :
\[\left( x+2 \right)\frac{dy}{dx}={{x}^{2}}+4x-9x\ne -2\] \[\frac{dy}{dx}=\frac{{{x}^{2}}+4x-9}{x+2}\] \[dy=\frac{{{x}^{2}}+4x-9}{x+2}dx\] \[\int_{{}}^{{}}{dy=\int_{{}}^{{}}{\frac{{{x}^{2}}+4x-9}{x+2}}dx}\] \[y=\int_{{}}^{{}}{\left( x+2-\frac{13}{x+2} \right)dx}\] \[y=\int_{{}}^{{}}{\left( x+2 \right)dx-13\int_{{}}^{{}}{\frac{1}{x+2}dx}}\] \[y=\frac{{{x}^{2}}}{2}+2x-13\log \left| x+2 \right|+c\] Given that y = (0) = 0 \[0=-13\log z+c\] \[y=\frac{{{x}^{2}}}{2}+2x-13\log \left| x+2 \right|+13\log 2\] \[y\left( -4 \right)=8-8-13\log 2+13\log 2=0\]
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