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 = 0.163746 (sec), leaf count = 89
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.115 (sec), leaf count = 33
\[\left [y \left (x \right ) = \ln \left (x +\sqrt {x^{2}-1}\right )+\textit {\_C1}, y \left (x \right ) = -\ln \left (x +\sqrt {x^{2}-1}\right )+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[Sqrt[1 + y'[x]^2] == x*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] + Log[1 - x/Sqrt[-1 + x^2]] - Log[1 + x/Sqrt[-1 + x^2]])/2}, {y[x] -> (2*C[1] - Log[1 - x/Sqrt[-1 + x^2]] + Log[1 + x/Sqrt[-1 + x^2]])/2}}
Maple raw input
dsolve((1+diff(y(x),x)^2)^(1/2) = x*diff(y(x),x), y(x))
Maple raw output
[y(x) = ln(x+(x^2-1)^(1/2))+_C1, y(x) = -ln(x+(x^2-1)^(1/2))+_C1]