Internal problem ID [6871]
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]
\[ \boxed {y^{2} {y^{\prime }}^{2}-y \left (x +1\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) &= \sqrt {c_{1} +2 x} \\ y \left (x \right ) &= -\sqrt {c_{1} +2 x} \\ y \left (x \right ) &= \sqrt {x^{2}+c_{1}} \\ y \left (x \right ) &= -\sqrt {x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 72
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} \sqrt {x+c_1} \\ y(x)\to \sqrt {2} \sqrt {x+c_1} \\ y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ \end{align*}