60.2.402 problem 979

Internal problem ID [10989]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 979
Date solved : Monday, January 27, 2025 at 10:38:51 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Abel]

\begin{align*} y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 49

dsolve(diff(y(x),x) = (y(x)^3-3*x*y(x)^2+3*x^2*y(x)-x^3+x)/x,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {-2 \ln \left (x \right )+c_{1}}\, x -1}{\sqrt {-2 \ln \left (x \right )+c_{1}}} \\ y &= \frac {\sqrt {-2 \ln \left (x \right )+c_{1}}\, x +1}{\sqrt {-2 \ln \left (x \right )+c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 42

DSolve[D[y[x],x] == (x - x^3 + 3*x^2*y[x] - 3*x*y[x]^2 + y[x]^3)/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x-\frac {1}{\sqrt {-2 \log (x)+c_1}} \\ y(x)\to x+\frac {1}{\sqrt {-2 \log (x)+c_1}} \\ y(x)\to x \\ \end{align*}