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 = 0.150427 (sec), leaf count = 30
\[\left \{\left \{y(x)\to e^{-2 x} \left (c_3 e^{5 x}+c_2 \cos (x)+c_1 \sin (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 27
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{3 x}+\textit {\_C2} \,{\mathrm e}^{-2 x} \sin \left (x \right )+\textit {\_C3} \,{\mathrm e}^{-2 x} \cos \left (x \right )]\] 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))
Maple raw output
[y(x) = _C1*exp(3*x)+_C2*exp(-2*x)*sin(x)+_C3*exp(-2*x)*cos(x)]