40.6.3 problem 12

Internal problem ID [6683]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page 74
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:21:02 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+4 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+4*x=0,y(x), singsol=all)
 

\begin{align*} y &= -2 x \\ y &= 2 x \\ y &= \frac {4 c_1^{2}+x^{2}}{2 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.288 (sec). Leaf size: 43

DSolve[x*D[y[x],x]^2-2*y[x]*D[y[x],x]+4*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -2 x \cosh (-\log (x)+c_1) \\ y(x)\to -2 x \cosh (\log (x)+c_1) \\ y(x)\to -2 x \\ y(x)\to 2 x \\ \end{align*}