4.45.24 \(y''''(x)-2 y''(x)+y(x)=e^x+4\)

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 = 0.222797 (sec), leaf count = 45

\[\left \{\left \{y(x)\to e^x \left (\frac {x^2}{8}+\left (-\frac {1}{4}+c_4\right ) x+\frac {3}{16}+c_3\right )+e^{-x} (c_2 x+c_1)+4\right \}\right \}\]

Maple ✓
cpu = 0.078 (sec), leaf count = 44

\[\left [y \left (x \right ) = \frac {x^{2} {\mathrm e}^{x}}{8}-\frac {x \,{\mathrm e}^{x}}{4}+4+\frac {3 \,{\mathrm e}^{x}}{16}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-x}+\textit {\_C3} x \,{\mathrm e}^{x}+\textit {\_C4} x \,{\mathrm e}^{-x}\right ]\] Mathematica raw input

DSolve[y[x] - 2*y''[x] + y''''[x] == 4 + E^x,y[x],x]

Mathematica raw output

{{y[x] -> 4 + (C[1] + x*C[2])/E^x + E^x*(3/16 + x^2/8 + C[3] + x*(-1/4 + C[4]))}
}

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))

Maple raw output

[y(x) = 1/8*x^2*exp(x)-1/4*x*exp(x)+4+3/16*exp(x)+_C1*exp(x)+_C2*exp(-x)+_C3*x*e
xp(x)+_C4*x*exp(-x)]