4.19.23 $(a^2-x^2)y^{\prime }(x{)}^2=x^2$

ODE
$$(a^2-x^2)y^{\prime }(x{)}^2=x^2$$ ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $y^{\prime }$

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

$$\{\{y(x)\to c_1-\sqrt{a^2-x^2}\},\{y(x)\to \sqrt{a^2-x^2}+c_1\}\}$$

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

$$\{y\left(x\right)=-(a-x)(a+x)\frac{1}{\sqrt{(a-x)(a+x)}}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=(a-x)(a+x)\frac{1}{\sqrt{(a-x)(a+x)}}+\mathit{\_}\mathit{C}\mathit{1}\}$$ 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