54.2.7 problem 8

Internal problem ID [8539]
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
Date solved : Monday, January 27, 2025 at 04:11:23 PM
CAS classification : [_quadrature]

\begin{align*} y^{2} {y^{\prime }}^{2}-y \left (1+x \right ) y^{\prime }+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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 &= \sqrt {c_{1} +2 x} \\ y &= -\sqrt {c_{1} +2 x} \\ y &= \sqrt {x^{2}+c_{1}} \\ y &= -\sqrt {x^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 72

DSolve[y[x]^2*(D[y[x],x])^2-y[x]*(x+1)*D[y[x],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*}