4.19.23 \(\left (a^2-x^2\right ) y'(x)^2=x^2\)

ODE
\[ \left (a^2-x^2\right ) y'(x)^2=x^2 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Mathematica
cpu = 0.00876538 (sec), leaf count = 43

\[\left \{\left \{y(x)\to c_1-\sqrt {a^2-x^2}\right \},\left \{y(x)\to \sqrt {a^2-x^2}+c_1\right \}\right \}\]

Maple
cpu = 0.035 (sec), leaf count = 52

\[ \left \{ y \relax (x ) =-{ \left (a-x \right ) \left (a+x \right ) {\frac {1}{\sqrt { \left (a-x \right ) \left (a+x \right ) }}}}+{\it \_C1},y \relax (x ) ={ \left (a-x \right ) \left (a+x \right ) {\frac {1}{\sqrt { \left (a-x \right ) \left (a+x \right ) }}}}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[(a^2 - x^2)*y'[x]^2 == x^2,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[a^2 - x^2] + C[1]}, {y[x] -> Sqrt[a^2 - x^2] + C[1]}}

Maple raw input

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

Maple raw output

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