4.16.14 \(y'(x)^2=x^2 y(x)^2\)

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

[_separable]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 0.00432521 (sec), leaf count = 33

\[\left \{\left \{y(x)\to c_1 e^{-\frac {x^2}{2}}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 23

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{-{\frac {{x}^{2}}{2}}}},y \relax (x ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right \} \] Mathematica raw input

DSolve[y'[x]^2 == x^2*y[x]^2,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = _C1*exp(1/2*x^2), y(x) = _C1*exp(-1/2*x^2)