4.16.12 \(y'(x)^2=a^2 y(x)^2\)

ODE
\[ y'(x)^2=a^2 y(x)^2 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Mathematica
cpu = 0.00433385 (sec), leaf count = 26

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

Maple
cpu = 0.007 (sec), leaf count = 20

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{ax}},y \relax (x ) ={\it \_C1}\,{{\rm e}^{-ax}} \right \} \] Mathematica raw input

DSolve[y'[x]^2 == a^2*y[x]^2,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x)^2 = a^2*y(x)^2, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(a*x), y(x) = _C1*exp(-a*x)