ODE
\[ -a^2+y(x)^2 y'(x)^2+y(x)^2=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.0205655 (sec), leaf count = 89
\[\left \{\left \{y(x)\to -\sqrt {a^2-\left (c_1+x\right ){}^2}\right \},\left \{y(x)\to \sqrt {a^2-\left (c_1+x\right ){}^2}\right \},\left \{y(x)\to -\sqrt {a^2-\left (x-c_1\right ){}^2}\right \},\left \{y(x)\to \sqrt {a^2-\left (x-c_1\right ){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.687 (sec), leaf count = 76
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2}=0,x-{ \left ( a-y \left ( x \right ) \right ) \left ( a+y \left ( x \right ) \right ) {\frac {1}{\sqrt { \left ( a-y \left ( x \right ) \right ) \left ( a+y \left ( x \right ) \right ) }}}}-{\it \_C1}=0,x+{ \left ( a-y \left ( x \right ) \right ) \left ( a+y \left ( x \right ) \right ) {\frac {1}{\sqrt { \left ( a-y \left ( x \right ) \right ) \left ( a+y \left ( x \right ) \right ) }}}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[-a^2 + y[x]^2 + y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[a^2 - (x + C[1])^2]}, {y[x] -> Sqrt[a^2 - (x + C[1])^2]}, {y[x] -> -Sqrt[a^2 - (x - C[1])^2]}, {y[x] -> Sqrt[a^2 - (x - C[1])^2]}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2-a^2+y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x)^2-a^2 = 0, x+(a-y(x))*(a+y(x))/((a-y(x))*(a+y(x)))^(1/2)-_C1 = 0, x-(a-y(x))*(a+y(x))/((a-y(x))*(a+y(x)))^(1/2)-_C1 = 0