15.21.9 problem 31

Internal problem ID [3333]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 31
Date solved : Monday, January 27, 2025 at 07:34:23 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 57

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

\begin{align*} y(x)\to c_1 x-\frac {2}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 i \sqrt {2} \sqrt {x} \\ y(x)\to 2 i \sqrt {2} \sqrt {x} \\ \end{align*}