Internal problem ID [2333]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 20.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _dAlembert]
\[ \boxed {-y {y^{\prime }}^{2}=-8 x -1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 135
dsolve(8*x+1=diff(y(x),x)^2*y(x),y(x), singsol=all)
\begin{align*} \frac {\left (-64 x -8\right ) c_{1}}{\left (\frac {8 x +1-2 \sqrt {y \left (x \right ) \left (8 x +1\right )}+4 y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}} y \left (x \right ) \left (\frac {-\sqrt {y \left (x \right ) \left (8 x +1\right )}-2 y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}}}+x +\frac {1}{8} = 0 \frac {\left (-64 x -8\right ) c_{1}}{\left (\frac {8 x +1+2 \sqrt {y \left (x \right ) \left (8 x +1\right )}+4 y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}} y \left (x \right ) \left (\frac {\sqrt {y \left (x \right ) \left (8 x +1\right )}-2 y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}}}+x +\frac {1}{8} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 3.669 (sec). Leaf size: 79
DSolve[8*x+1==y'[x]^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-8 \sqrt {8 x+1} x-\sqrt {8 x+1}+12 c_1\right ){}^{2/3} y(x)\to \frac {1}{4} \left (8 \sqrt {8 x+1} x+\sqrt {8 x+1}+12 c_1\right ){}^{2/3} \end{align*}