60.1.176 problem 177

Internal problem ID [10190]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 177
Date solved : Monday, January 27, 2025 at 06:36:16 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \frac {x^{2}}{1+c_{1} \left (x -1\right )} \]

✓ Solution by Mathematica

Time used: 0.332 (sec). Leaf size: 160

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

\begin{align*} y(x)\to \frac {\exp \left (\int _1^x\frac {K[1]-2}{(K[1]-1) K[1]}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {K[1]-2}{(K[1]-1) K[1]}dK[1]\right )}{(K[2]-1) K[2]^2}dK[2]+c_1} \\ y(x)\to 0 \\ y(x)\to -\frac {\exp \left (\int _1^x\frac {K[1]-2}{(K[1]-1) K[1]}dK[1]\right )}{\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {K[1]-2}{(K[1]-1) K[1]}dK[1]\right )}{(K[2]-1) K[2]^2}dK[2]} \\ \end{align*}