Let g be a differentiable function such that ₀^x g(t) d t=x- ₀^x tg (t) d t, x 0 and let y=y(x) satisfy the differential equation d y d x -y x=2(x+1) x g(x), x [0, 2 ) . If y(0)=0 , then y ( 3 ) is equal to

Step-by-step solution

Diff. w.r.t. x aligned & g(x)=1-x g(x) & g(x)= 1 1+x & so d y d x -y x=2 x & I F=e^ - d x =e^ x = x aligned solution of D.E. aligned & y x= 2 d x+c & y x=2 x+c & y(0)=0 aligned c =0 aligned & y= 2 x x & y=2 x x & y ( 3 )=2 3 2= 4 3 aligned