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 = 0.0915032 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {1}{32} e^{2 x} \left (16 c_1-12 x+9\right )-\frac {1}{2} c_2 e^{-2 x}+c_3-\frac {x^3}{12}-\frac {x}{8}\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -36\,x+48\,{\it \_C2}+27 \right ) {{\rm e}^{2\,x}}}{96}}-{\frac {{x}^{3}}{12}}-{\frac {{{\rm e}^{-2\,x}}{\it \_C1}}{2}}-{\frac {x}{8}}+{\it \_C3} \right \} \] Mathematica raw input
DSolve[-4*y'[x] + y'''[x] == -3*E^(2*x) + x^2,y[x],x]
Mathematica raw output
{{y[x] -> -x/8 - 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),'implicit')
Maple raw output
y(x) = 1/96*(-36*x+48*_C2+27)*exp(2*x)-1/12*x^3-1/2*exp(-2*x)*_C1-1/8*x+_C3