60.2.203 problem 779

Internal problem ID [10790]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 779
Date solved : Monday, January 27, 2025 at 09:44:37 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Abel]

\begin{align*} y^{\prime }&=\frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.149 (sec). Leaf size: 50

dsolve(diff(y(x),x) = 1/(x-1)*(x^3*y(x)+x^3+x*y(x)^2+y(x)^3)/x^3,y(x), singsol=all)
 

\[ \frac {\ln \left (\frac {x +y}{x}\right )}{2}-\frac {\ln \left (\frac {x^{2}+y^{2}}{x^{2}}\right )}{4}+\frac {\arctan \left (\frac {y}{x}\right )}{2}-\ln \left (x -1\right )+\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 52

DSolve[D[y[x],x] == (x^3 + x^3*y[x] + x*y[x]^2 + y[x]^3)/((-1 + x)*x^3),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{(K[1]+1) \left (K[1]^2+1\right )}dK[1]=\int _1^x\frac {1}{(K[2]-1) K[2]}dK[2]+c_1,y(x)\right ] \]