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