Internal problem ID [2343]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 38, page 173
Problem number: 6.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y \left ({y^{\prime }}^{2}+1\right )-2 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 75
dsolve((diff(y(x),x)^2+1)*y(x)=2*diff(y(x),x)*x,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x y \left (x \right ) = x y \left (x \right ) = 0 y \left (x \right ) = \sqrt {-2 c_{1} x i+c_{1}^{2}} y \left (x \right ) = \sqrt {2 c_{1} x i+c_{1}^{2}} y \left (x \right ) = -\sqrt {-2 c_{1} x i+c_{1}^{2}} y \left (x \right ) = -\sqrt {2 c_{1} x i+c_{1}^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 1.091 (sec). Leaf size: 174
DSolve[(y'[x]^2+1)*y[x]==2*y'[x]*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} \left (\cosh \left (\frac {c_1}{2}\right )+\sinh \left (\frac {c_1}{2}\right )\right ) \sqrt {-8 i x+\cosh (c_1)+\sinh (c_1)} y(x)\to \frac {1}{4} \left (\cosh \left (\frac {c_1}{2}\right )+\sinh \left (\frac {c_1}{2}\right )\right ) \sqrt {-8 i x+\cosh (c_1)+\sinh (c_1)} y(x)\to -\frac {1}{4} \left (\cosh \left (\frac {c_1}{2}\right )+\sinh \left (\frac {c_1}{2}\right )\right ) \sqrt {8 i x+\cosh (c_1)+\sinh (c_1)} y(x)\to \frac {1}{4} \left (\cosh \left (\frac {c_1}{2}\right )+\sinh \left (\frac {c_1}{2}\right )\right ) \sqrt {8 i x+\cosh (c_1)+\sinh (c_1)} y(x)\to 0 y(x)\to -x y(x)\to x \end{align*}