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 = 0.176457 (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 = 0.01 (sec), leaf count = 20
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{a x}, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-a x}]\] 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))
Maple raw output
[y(x) = _C1*exp(a*x), y(x) = _C1*exp(-a*x)]