ODE
\[ a y'(x)+b y(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.150631 (sec), leaf count = 47
\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )} \left (c_2 e^{x \sqrt {a^2-4 b}}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 45
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\left (-\frac {a}{2}+\frac {\sqrt {a^{2}-4 b}}{2}\right ) x}+\textit {\_C2} \,{\mathrm e}^{\left (-\frac {a}{2}-\frac {\sqrt {a^{2}-4 b}}{2}\right ) x}\right ]\] Mathematica raw input
DSolve[b*y[x] + a*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + E^(Sqrt[a^2 - 4*b]*x)*C[2])/E^(((a + Sqrt[a^2 - 4*b])*x)/2)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)+b*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp((-1/2*a+1/2*(a^2-4*b)^(1/2))*x)+_C2*exp((-1/2*a-1/2*(a^2-4*b)^(1/2))*x)]