ODE
\[ y''''(x)-2 y''(x)+y(x)=e^x+4 \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0528111 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \frac {1}{16} e^{-x} \left (e^{2 x} \left (4 \left (4 c_4-1\right ) x+16 c_3+2 x^2+3\right )+16 \left (c_2 x+c_1\right )+64 e^x\right )\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 16\,{\it \_C4}\,x+16\,{\it \_C2} \right ) {{\rm e}^{-x}}}{16}}+4+{\frac { \left ( 2\,{x}^{2}+ \left ( 16\,{\it \_C3}-4 \right ) x+16\,{\it \_C1}+3 \right ) {{\rm e}^{x}}}{16}} \right \} \] Mathematica raw input
DSolve[y[x] - 2*y''[x] + y''''[x] == 4 + E^x,y[x],x]
Mathematica raw output
{{y[x] -> (64*E^x + 16*(C[1] + x*C[2]) + E^(2*x)*(3 + 2*x^2 + 16*C[3] + 4*x*(-1 + 4*C[4])))/(16*E^x)}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)+y(x) = 4+exp(x), y(x),'implicit')
Maple raw output
y(x) = 1/16*(16*_C4*x+16*_C2)*exp(-x)+4+1/16*(2*x^2+(16*_C3-4)*x+16*_C1+3)*exp(x)