4.5.24 \((x+1) y'(x)=(3 x+4) x^3+y(x)\)

ODE
\[ (x+1) y'(x)=(3 x+4) x^3+y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0164465 (sec), leaf count = 18

\[\left \{\left \{y(x)\to \left (c_1+4\right ) x+c_1+x^4+4\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 14

\[ \left \{ y \relax (x ) ={x}^{4}+{\it \_C1}\,x+{\it \_C1}+x+1 \right \} \] Mathematica raw input

DSolve[(1 + x)*y'[x] == x^3*(4 + 3*x) + y[x],y[x],x]

Mathematica raw output

{{y[x] -> 4 + x^4 + C[1] + x*(4 + C[1])}}

Maple raw input

dsolve((1+x)*diff(y(x),x) = x^3*(4+3*x)+y(x), y(x),'implicit')

Maple raw output

y(x) = x^4+_C1*x+_C1+x+1