ODE
\[ y'(x)^2=x^2 y(x)^2 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.170011 (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 = 0.01 (sec), leaf count = 23
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x^{2}}{2}}, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {x^{2}}{2}}\right ]\] 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))
Maple raw output
[y(x) = _C1*exp(1/2*x^2), y(x) = _C1*exp(-1/2*x^2)]