ODE
\[ y'''(x)=y(x)+e^x x+\cos ^2(x) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 4.51196 (sec), leaf count = 265
\[\left \{\left \{y(x)\to e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right ) \int _1^x-\frac {e^{\frac {K[1]}{2}} \left (\cos (2 K[1])+2 e^{K[1]} K[1]+1\right ) \left (\sqrt {3} \cos \left (\frac {1}{2} \sqrt {3} K[1]\right )-3 \sin \left (\frac {1}{2} \sqrt {3} K[1]\right )\right )}{6 \sqrt {3}}dK[1]+e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \int _1^x-\frac {e^{\frac {K[2]}{2}} \left (\cos (2 K[2])+2 e^{K[2]} K[2]+1\right ) \left (3 \cos \left (\frac {1}{2} \sqrt {3} K[2]\right )+\sqrt {3} \sin \left (\frac {1}{2} \sqrt {3} K[2]\right )\right )}{6 \sqrt {3}}dK[2]+\frac {e^x x^2}{6}+\frac {1}{15} \sin (2 x)-\frac {1}{30} \cos (2 x)+c_1 e^x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-\frac {1}{6}\right \}\right \}\]
Maple ✓
cpu = 13.009 (sec), leaf count = 121
\[\left [y \left (x \right ) = \frac {\cos \left (2 x \right )}{10 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}+\frac {4 \sin \left (2 x \right )}{5 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}-\frac {13 \left (3 x^{2} {\mathrm e}^{x}-6 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x}-9\right )}{18 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\textit {\_C3} \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )\right ]\] Mathematica raw input
DSolve[y'''[x] == E^x*x + Cos[x]^2 + y[x],y[x],x]
Mathematica raw output
{{y[x] -> -1/6 + (E^x*x^2)/6 + E^x*C[1] - Cos[2*x]/30 + (C[2]*Cos[(Sqrt[3]*x)/2])/E^(x/2) + Sin[2*x]/15 + (C[3]*Sin[(Sqrt[3]*x)/2])/E^(x/2) + (Cos[(Sqrt[3]*x)/2]*Inactive[Integrate][-1/6*(E^(K[1]/2)*(1 + Cos[2*K[1]] + 2*E^K[1]*K[1])*(Sqrt[3]*Cos[(Sqrt[3]*K[1])/2] - 3*Sin[(Sqrt[3]*K[1])/2]))/Sqrt[3], {K[1], 1, x}])/E^(x/2) + (Sin[(Sqrt[3]*x)/2]*Inactive[Integrate][-1/6*(E^(K[2]/2)*(1 + Cos[2*K[2]] + 2*E^K[2]*K[2])*(3*Cos[(Sqrt[3]*K[2])/2] + Sqrt[3]*Sin[(Sqrt[3]*K[2])/2]))/Sqrt[3], {K[2], 1, x}])/E^(x/2)}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = x*exp(x)+cos(x)^2+y(x), y(x))
Maple raw output
[y(x) = 1/10/(5+2*3^(1/2))/(-5+2*3^(1/2))*cos(2*x)+4/5/(5+2*3^(1/2))/(-5+2*3^(1/2))*sin(2*x)-13/18*(3*x^2*exp(x)-6*x*exp(x)+4*exp(x)-9)/(5+2*3^(1/2))/(-5+2*3^(1/2))+_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)]