Question

If $y\left(x\right)$ is the solution of the differential equation
$(x+2)\frac{dy}{dx}=x^2+4x–9,x\ne –2$
$\text{and}y\left(0\right)=0,\text{then}y(–4)$is equal to :

• A. $2$
• B. $0$
• C. $-1$
• D. $1$

Answer 1

The correct option is B $0$

$(x+2)\frac{dy}{dx}=x^2+4x–9\frac{dy}{dx}=\frac{x^2+4x–9+4-4}{x+2}\frac{dy}{dx}=\frac{(x+2{)}^2-13}{x+2}\int dy=\int \left[\right(x+2)-\frac{13}{x+2}]dxy=\frac{x^2}{2}+2x-13\ln |(x+2)|+C\text{Put}x=0,y=0C=13\ln 2y=\frac{x^2}{2}+2x-13\ln |(x+2)|+13\ln 2y(-4)=0$