ODE
\[ y''''(x)+3 y''(x)-4 y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00871098 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_3 e^{-x}+c_4 e^x+c_2 \sin (2 x)+c_1 \cos (2 x)\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}}+{\it \_C2}\,{{\rm e}^{x}}+{\it \_C3}\,\sin \left ( 2\,x \right ) +{\it \_C4}\,\cos \left ( 2\,x \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*exp(-x)+_C2*exp(x)+_C3*sin(2*x)+_C4*cos(2*x)