Internal problem ID [6118]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 8.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}-y \left (1+x \right ) y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 45
dsolve(y(x)^2*diff(y(x),x)^2-y(x)*(x+1)*diff(y(x),x)+x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2 x +c_{1}} \\ y \relax (x ) = -\sqrt {2 x +c_{1}} \\ y \relax (x ) = \sqrt {x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 61
DSolve[y[x]^2*(y'[x])^2-y[x]*(x+1)*y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2 x+c_1} \\ y(x)\to \sqrt {2 x+c_1} \\ y(x)\to -\sqrt {x^2+c_1} \\ y(x)\to \sqrt {x^2+c_1} \\ \end{align*}