ODE
\[ y''(x)=\text {c1} e^{a x}+\text {c2} e^{-b x} \] ODE Classification
[[_2nd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.181132 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {\text {c1} e^{a x}}{a^2}+\frac {\text {c2} e^{-b x}}{b^2}+c_2 x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.072 (sec), leaf count = 28
\[\left [y \left (x \right ) = \frac {\mathit {c1} \,{\mathrm e}^{a x}}{a^{2}}+\frac {\mathit {c2} \,{\mathrm e}^{-b x}}{b^{2}}+\textit {\_C1} x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y''[x] == c1*E^(a*x) + c2/E^(b*x),y[x],x]
Mathematica raw output
{{y[x] -> (c1*E^(a*x))/a^2 + c2/(b^2*E^(b*x)) + C[1] + x*C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = c1*exp(a*x)+c2*exp(-b*x), y(x))
Maple raw output
[y(x) = c1/a^2*exp(a*x)+c2/b^2*exp(-b*x)+_C1*x+_C2]