ODE
\[ \left (a^2+x^2\right ) y'(x)^2=b^2 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.0179269 (sec), leaf count = 48
\[\left \{\left \{y(x)\to c_1-b \log \left (\sqrt {a^2+x^2}+x\right )\right \},\left \{y(x)\to b \log \left (\sqrt {a^2+x^2}+x\right )+c_1\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) =-b\ln \left ( x+\sqrt {{a}^{2}+{x}^{2}} \right ) +{\it \_C1},y \left ( x \right ) =b\ln \left ( x+\sqrt {{a}^{2}+{x}^{2}} \right ) +{\it \_C1} \right \} \] Mathematica raw input
DSolve[(a^2 + x^2)*y'[x]^2 == b^2,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, 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