4.19.21 \(\left (a^2-x^2\right ) y'(x)^2+b^2=0\)

ODE
\[ \left (a^2-x^2\right ) y'(x)^2+b^2=0 \] ODE Classification

[_quadrature]

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

Mathematica
cpu = 0.0201466 (sec), leaf count = 52

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

Maple
cpu = 0.037 (sec), leaf count = 44

\[ \left \{ y \relax (x ) =-b\ln \left (x+\sqrt {-{a}^{2}+{x}^{2}} \right ) +{\it \_C1},y \relax (x ) =b\ln \left (x+\sqrt {-{a}^{2}+{x}^{2}} \right ) +{\it \_C1} \right \} \] Mathematica raw input

DSolve[b^2 + (a^2 - x^2)*y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve((a^2-x^2)*diff(y(x),x)^2+b^2 = 0, y(x),'implicit')

Maple raw output

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