the answer should be

-x^e(-4x) -1/7e^(-4x)+1/7 e^(3x)

u1 ' = -1 u1 = -x +A

u2 ' = e^(-7x) u2 = -1/7e^(-7x) + B

y = -xe^(-4x) - 1/7 e^(-7x) + A e^(-4x) + B e^(3x)

Applying IC A + B = 1/7

-4A + 3B = 3/7

Multiply the top by 4 and add to the bottom you get B = 1/7, A = 0

-x^e(-4x) -1/7e^(-4x)+1/7 e^(3x) follows