ODE
\[ y'''(x)-4 y'(x)=x^2-3 e^{2 x} \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.265026 (sec), leaf count = 49
\[\left \{\left \{y(x)\to -\frac {x^3}{12}-\frac {x}{8}+\frac {1}{32} e^{2 x} (-12 x+9+16 c_1)-\frac {1}{2} c_2 e^{-2 x}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.262 (sec), leaf count = 41
\[\left [y \left (x \right ) = -\frac {\textit {\_C2} \,{\mathrm e}^{-2 x}}{2}+\frac {{\mathrm e}^{2 x} \textit {\_C1}}{2}-\frac {x^{3}}{12}-\frac {3 \,{\mathrm e}^{2 x} x}{8}+\frac {9 \,{\mathrm e}^{2 x}}{32}-\frac {x}{8}+\textit {\_C3}\right ]\] Mathematica raw input
DSolve[-4*y'[x] + y'''[x] == -3*E^(2*x) + x^2,y[x],x]
Mathematica raw output
{{y[x] -> -1/8*x - x^3/12 + (E^(2*x)*(9 - 12*x + 16*C[1]))/32 - C[2]/(2*E^(2*x)) + C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-4*diff(y(x),x) = x^2-3*exp(2*x), y(x))
Maple raw output
[y(x) = -1/2*_C2*exp(-2*x)+1/2*exp(2*x)*_C1-1/12*x^3-3/8*exp(2*x)*x+9/32*exp(2*x)-1/8*x+_C3]