Let f be a differentiable function such that 2(x+2)^2 f(x)-3(x+2)^2=10 ₀^x(t+2) f(t) d t, x 0 . Then f(2) is equal to ______.

Step-by-step solution

2(x+2)^2 f(x)-3(x+2)^2=10 ₀^x(t+2) f(t) d t Differentiating both side aligned & 4(x+2) f(x)+2 f(x)(x+2)^2-6(x+2)=10(x+2) f(x) & =(x+2) d y d x -3 y=3 & 1 3 d y y+1 = d x x+2 & |y+1=3 | x+2 + c & y+1=(x+2)^3 c & y(0)= 3 2 & 5 16 =c & y= 5 16 (x+2)^3-1 & y(2)= 5 16 64-1=19 aligned