El profesor se sorprenderá mucho al ver tu solución correcta😉
d 2 --(y(x)) = (1 + x + y(x)) dx
y' = (x + y + 1)^2
f1(x)*g1(u)*u' = f2(x)*g2(u),
g1(u)/g2(u)*u'= f2(x)/f1(x).
3 / 2 2 / 2 \ / 2 2\\ 4 / / 2 2\ / 2 \ / / 2 2\ / 2 \\ / 2 \\ 5 / 2 2 / / 2 2\ / 2 \\ / 2 \ / 2 2\ / 2 \ / 2 2 / / 2 2\ / 2 \\ / 2 \ / 2 2\\\ / 2 \ 2 / / 2 \\ x *\2 + C1 + 2*C1 + 2*(1 + C1) + \1 + C1 + 2*C1/*\2 + C1 + 2*C1 + 2*(1 + C1) // x *\3 + 3*C1 + (1 + C1)*\2 + C1 + 2*C1 + 2*(1 + C1) / + \1 + C1 + 2*C1/*\3 + 3*C1 + (1 + C1)*\2 + C1 + 2*C1 + 2*(1 + C1) / + 3*(1 + C1)*\1 + C1 + 2*C1// + 3*(1 + C1)*\1 + C1 + 2*C1// x *\4 + 2*C1 + 4*C1 + 7*(1 + C1) + (1 + C1)*\3 + 3*C1 + (1 + C1)*\2 + C1 + 2*C1 + 2*(1 + C1) / + 3*(1 + C1)*\1 + C1 + 2*C1// + \1 + C1 + 2*C1/*\4 + 2*C1 + 4*C1 + 7*(1 + C1) / + \1 + C1 + 2*C1/*\4 + 2*C1 + 4*C1 + 7*(1 + C1) + (1 + C1)*\3 + 3*C1 + (1 + C1)*\2 + C1 + 2*C1 + 2*(1 + C1) / + 3*(1 + C1)*\1 + C1 + 2*C1// + \1 + C1 + 2*C1/*\4 + 2*C1 + 4*C1 + 7*(1 + C1) /// / 6\ y(x) = C1 + x*\1 + C1 + 2*C1/ + x *\1 + C1 + (1 + C1)*\1 + C1 + 2*C1// + ----------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x / 3 6 15