4.5.25 \((x+1) y'(x)=2 y(x)+(x+1)^4\)

ODE
\[ (x+1) y'(x)=2 y(x)+(x+1)^4 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00532228 (sec), leaf count = 22

\[\left \{\left \{y(x)\to (x+1)^2 \left (c_1+\frac {x^2}{2}+x\right )\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 18

\[ \left \{ y \relax (x ) = \left (x+{\frac {{x}^{2}}{2}}+{\it \_C1} \right ) \left (1+x \right ) ^{2} \right \} \] Mathematica raw input

DSolve[(1 + x)*y'[x] == (1 + x)^4 + 2*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (1 + x)^2*(x + x^2/2 + C[1])}}

Maple raw input

dsolve((1+x)*diff(y(x),x) = (1+x)^4+2*y(x), y(x),'implicit')

Maple raw output

y(x) = (x+1/2*x^2+_C1)*(1+x)^2