29.31.2 problem 901

Internal problem ID [5481]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 901
Date solved : Monday, January 27, 2025 at 11:27:10 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.917 (sec). Leaf size: 64

DSolve[x^2 (D[y[x],x])^2-(a+2 x y[x])D[y[x],x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x-2 \sqrt {a} c_1}{4 c_1{}^2} \\ y(x)\to \frac {x+2 \sqrt {a} c_1}{4 c_1{}^2} \\ y(x)\to 0 \\ y(x)\to -\frac {a}{4 x} \\ \end{align*}