ODE
\[ \sqrt {y'(x)^2+1}=x y'(x) \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.0206125 (sec), leaf count = 41
\[\left \{\left \{y(x)\to c_1-\log \left (\sqrt {x^2-1}+x\right )\right \},\left \{y(x)\to c_1+\log \left (\sqrt {x^2-1}+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.04 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) =-\ln \left ( x+\sqrt {{x}^{2}-1} \right ) +{\it \_C1},y \left ( x \right ) =\ln \left ( x+\sqrt {{x}^{2}-1} \right ) +{\it \_C1} \right \} \] Mathematica raw input
DSolve[Sqrt[1 + y'[x]^2] == x*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1] - Log[x + Sqrt[-1 + x^2]]}, {y[x] -> C[1] + Log[x + Sqrt[-1 + x^2]]}}
Maple raw input
dsolve((1+diff(y(x),x)^2)^(1/2) = x*diff(y(x),x), y(x),'implicit')
Maple raw output
y(x) = ln(x+(x^2-1)^(1/2))+_C1, y(x) = -ln(x+(x^2-1)^(1/2))+_C1