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]
\[ \boxed {y \left (1+{y^{\prime }}^{2}\right )-2 x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 71
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 {c_{1} \left (-2 i x +c_{1} \right )} \\ y \left (x \right ) &= \sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ \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*}