60.1.255 problem 256

Internal problem ID [10269]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 256
Date solved : Monday, January 27, 2025 at 06:42:44 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 33

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

\[ y = x \,{\mathrm e}^{\frac {-\operatorname {LambertW}\left (-x \,{\mathrm e}^{\frac {c_{1} x +1}{x}}\right ) x +c_{1} x +1}{x}} \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]}dK[1]\&\right ]\left [-\frac {1}{x}-\log (x)+1+c_1\right ] \\ y(x)\to 0 \\ \end{align*}