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 = 0.0431898 (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 = 0.012 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {{\it c1}\,{{\rm e}^{ax}}}{{a}^{2}}}+{\frac {{\it c2}\,{{\rm e}^{-bx}}}{{b}^{2}}}+{\it \_C1}\,x+{\it \_C2} \right \} \] 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),'implicit')
Maple raw output
y(x) = c1/a^2*exp(a*x)+c2/b^2*exp(-b*x)+_C1*x+_C2