ODE
\[ y'''(x)=x^2+y(x) \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00995989 (sec), leaf count = 59
\[\left \{\left \{y(x)\to c_1 e^x+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )-x^2\right \}\right \}\]
Maple ✓
cpu = 0.121 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) =-{x}^{2}+{\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{{\rm e}^{-{\frac {x}{2}}}}\cos \left ( {\frac {\sqrt {3}x}{2}} \right ) +{\it \_C3}\,{{\rm e}^{-{\frac {x}{2}}}}\sin \left ( {\frac {\sqrt {3}x}{2}} \right ) \right \} \] Mathematica raw input
DSolve[y'''[x] == x^2 + y[x],y[x],x]
Mathematica raw output
{{y[x] -> -x^2 + E^x*C[1] + (C[2]*Cos[(Sqrt[3]*x)/2])/E^(x/2) + (C[3]*Sin[(Sqrt[3]*x)/2])/E^(x/2)}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = x^2+y(x), y(x),'implicit')
Maple raw output
y(x) = -x^2+_C1*exp(x)+_C2*exp(-1/2*x)*cos(1/2*3^(1/2)*x)+_C3*exp(-1/2*x)*sin(1/2*3^(1/2)*x)