60.1.485 problem 488

Internal problem ID [10499]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 488
Date solved : Monday, January 27, 2025 at 08:21:24 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 0.132 (sec). Leaf size: 72

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

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

✓ Solution by Mathematica

Time used: 0.691 (sec). Leaf size: 85

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

\begin{align*} y(x)\to -\frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a} \\ y(x)\to \frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a} \\ \end{align*}