4.36.22 \(y''(x)=a y(x)\)

ODE
\[ y''(x)=a y(x) \] ODE Classification

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.00753055 (sec), leaf count = 31

\[\left \{\left \{y(x)\to c_1 e^{\sqrt {a} x}+c_2 e^{-\sqrt {a} x}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 22

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\sqrt {a}x}}+{\it \_C2}\,{{\rm e}^{-\sqrt {a}x}} \right \} \] Mathematica raw input

DSolve[y''[x] == a*y[x],y[x],x]

Mathematica raw output

{{y[x] -> E^(Sqrt[a]*x)*C[1] + C[2]/E^(Sqrt[a]*x)}}

Maple raw input

dsolve(diff(diff(y(x),x),x) = a*y(x), y(x),'implicit')

Maple raw output

y(x) = _C1*exp(a^(1/2)*x)+_C2*exp(-a^(1/2)*x)