4.43.16 \(y'''(x)+y''(x)-7 y'(x)-15 y(x)=0\)

ODE
\[ y'''(x)+y''(x)-7 y'(x)-15 y(x)=0 \] ODE Classification

[[_3rd_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.0100837 (sec), leaf count = 30

\[\left \{\left \{y(x)\to e^{-2 x} \left (c_3 e^{5 x}+c_1 \sin (x)+c_2 \cos (x)\right )\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 27

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{3\,x}}+{\it \_C2}\,{{\rm e}^{-2\,x}}\sin \left ( x \right ) +{\it \_C3}\,{{\rm e}^{-2\,x}}\cos \left ( x \right ) \right \} \] Mathematica raw input

DSolve[-15*y[x] - 7*y'[x] + y''[x] + y'''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (E^(5*x)*C[3] + C[2]*Cos[x] + C[1]*Sin[x])/E^(2*x)}}

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-7*diff(y(x),x)-15*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(3*x)+_C2*exp(-2*x)*sin(x)+_C3*exp(-2*x)*cos(x)