ODE
\[ (x+1) y'(x)=(3 x+4) x^3+y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.175604 (sec), leaf count = 18
\[\left \{\left \{y(x)\to x^4+(4+c_1) x+4+c_1\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 15
\[[y \left (x \right ) = \left (1+x \right ) \textit {\_C1} +x^{4}+x +1]\] 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))
Maple raw output
[y(x) = (1+x)*_C1+x^4+x+1]