ODE
\[ 2 a y'(x)+b^2 y(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.156287 (sec), leaf count = 50
\[\left \{\left \{y(x)\to e^{-\left (x \left (\sqrt {a^2-b^2}+a\right )\right )} \left (c_2 e^{2 x \sqrt {a^2-b^2}}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 47
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\left (-a +\sqrt {a^{2}-b^{2}}\right ) x}+\textit {\_C2} \,{\mathrm e}^{\left (-a -\sqrt {a^{2}-b^{2}}\right ) x}\right ]\] Mathematica raw input
DSolve[b^2*y[x] + 2*a*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + E^(2*Sqrt[a^2 - b^2]*x)*C[2])/E^((a + Sqrt[a^2 - b^2])*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*a*diff(y(x),x)+b^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp((-a+(a^2-b^2)^(1/2))*x)+_C2*exp((-a-(a^2-b^2)^(1/2))*x)]