60.1.164 problem 165

Internal problem ID [10178]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 165
Date solved : Monday, January 27, 2025 at 06:31:26 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(x*(2*x-1)*diff(y(x),x) + y(x)^2 - (4*x+1)*y(x) + 4*x=0,y(x), singsol=all)
 

\[ y = \frac {2 x^{2}+c_{1}}{x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.418 (sec). Leaf size: 94

DSolve[x*(2*x-1)*D[y[x],x] + y[x]^2 - (4*x+1)*y[x] + 4*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1+\frac {\exp \left (\int _1^x\frac {1-4 K[1]}{K[1]-2 K[1]^2}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {1-4 K[1]}{K[1]-2 K[1]^2}dK[1]\right )}{K[2]-2 K[2]^2}dK[2]+c_1} \\ y(x)\to 1 \\ \end{align*}