If y( x ) is the solution of the differential equation (x+2) d y ~d x =x^2+4 x-9, x -2 and y(0)=0 , then y(-4) is equal to

Step-by-step solution

array ll & (x+2) d y ~d x =x^2+4 x-9 & ~d y= (x^2+4 x+4 )-4-9 x+2 ~d x & ~d y= (x+2)^2-13 (x+2) d x array Integrating both sides, we get aligned & d y= (x+2) d x-13 1 x+2 ~d x & y= (x+2)^2 2 -13 |x+2|+c...(i) aligned Given that y(0)=0 from equation (i), we get aligned & & 0 & =2-13 |0+2|+c ...(ii) & =13 (2)-2 aligned from (i) and (ii), we get y(-4)=2-13 (2)+13 (2)-2=0