60.1.433 problem 435

Internal problem ID [10447]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 435
Date solved : Monday, January 27, 2025 at 07:45:29 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.113 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+y(x)*(y(x)+1)-x = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 55

DSolve[-x + y[x]*(1 + y[x]) - 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 x+\frac {c_1{}^2 x}{4}-i c_1 \sqrt {x}-1 \\ y(x)\to x+\frac {c_1{}^2 x}{4}+i c_1 \sqrt {x}-1 \\ \end{align*}