ODE
\[ x^2 y'(x)^2-y(x)^4+y(x)^2=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.215409 (sec), leaf count = 73
\[\left \{\left \{y(x)\to -\sqrt {\sec ^2(-\log (x)+c_1)}\right \},\left \{y(x)\to \sqrt {\sec ^2(-\log (x)+c_1)}\right \},\left \{y(x)\to -\sqrt {\sec ^2(\log (x)+c_1)}\right \},\left \{y(x)\to \sqrt {\sec ^2(\log (x)+c_1)}\right \}\right \}\]
Maple ✓
cpu = 0.929 (sec), leaf count = 62
\[\left [y \left (x \right ) = -1, y \left (x \right ) = 1, y \left (x \right ) = \frac {\sqrt {\tan ^{2}\left (-\ln \left (x \right )+\textit {\_C1} \right )+1}}{\tan \left (-\ln \left (x \right )+\textit {\_C1} \right )}, y \left (x \right ) = -\frac {\sqrt {\tan ^{2}\left (-\ln \left (x \right )+\textit {\_C1} \right )+1}}{\tan \left (-\ln \left (x \right )+\textit {\_C1} \right )}\right ]\] Mathematica raw input
DSolve[y[x]^2 - y[x]^4 + x^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[Sec[C[1] - Log[x]]^2]}, {y[x] -> Sqrt[Sec[C[1] - Log[x]]^2]}, {y[x] -> -Sqrt[Sec[C[1] + Log[x]]^2]}, {y[x] -> Sqrt[Sec[C[1] + Log[x]]^2]}}
Maple raw input
dsolve(x^2*diff(y(x),x)^2+y(x)^2-y(x)^4 = 0, y(x))
Maple raw output
[y(x) = -1, y(x) = 1, y(x) = (tan(-ln(x)+_C1)^2+1)^(1/2)/tan(-ln(x)+_C1), y(x) = -(tan(-ln(x)+_C1)^2+1)^(1/2)/tan(-ln(x)+_C1)]