60.1.431 problem 433

Internal problem ID [10445]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 433
Date solved : Monday, January 27, 2025 at 07:45:23 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 36

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

\begin{align*} y &= \frac {-x^{2}-a}{x} \\ y &= \frac {c_{1}^{2}+4 c_{1} x -4 a}{4 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.908 (sec). Leaf size: 44

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

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