15.19.17 problem 17

Internal problem ID [3301]
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 : 17
Date solved : Monday, January 27, 2025 at 07:31:48 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 30

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

\begin{align*} y \left (x \right ) &= -2 x \\ y \left (x \right ) &= 2 x \\ y \left (x \right ) &= \frac {4 c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.327 (sec). Leaf size: 43

DSolve[4*x-2*D[y[x],x]*y[x]+D[y[x],x]^2*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*}