ODE
\[ y''''(x)+3 y''(x)-4 y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.146323 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_3 e^{-x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x)\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 27
\[[y \left (x \right ) = {\mathrm e}^{-x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{x}+\textit {\_C3} \sin \left (2 x \right )+\textit {\_C4} \cos \left (2 x \right )]\] Mathematica raw input
DSolve[-4*y[x] + 3*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3]/E^x + E^x*C[4] + C[1]*Cos[2*x] + C[2]*Sin[2*x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(y(x),x),x)-4*y(x) = 0, y(x))
Maple raw output
[y(x) = exp(-x)*_C1+_C2*exp(x)+_C3*sin(2*x)+_C4*cos(2*x)]