60.1.435 problem 437

Internal problem ID [10449]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 437
Date solved : Monday, January 27, 2025 at 07:45:43 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.312 (sec). Leaf size: 64

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