4.3.49 \(x y'(x)=x^3+y(x)+1\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00428841 (sec), leaf count = 18

\[\left \{\left \{y(x)\to c_1 x+\frac {x^3}{2}-1\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 14

\[ \left \{ y \relax (x ) ={\frac {{x}^{3}}{2}}-1+x{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -1 + x^3/2 + x*C[1]}}

Maple raw input

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

Maple raw output

y(x) = 1/2*x^3-1+x*_C1