60.2.197 problem 773

Internal problem ID [10784]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 773
Date solved : Monday, January 27, 2025 at 09:44:15 PM
CAS classification : [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.577 (sec). Leaf size: 58

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

\[ y = \frac {x \left (\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (2 \sqrt {3}\, \ln \left (2\right )-\sqrt {3}\, \ln \left (\frac {\sec \left (\textit {\_Z} \right )^{2} x^{2}}{\left (x -1\right )^{2}}\right )-\sqrt {3}\, \ln \left (3\right )+2 \sqrt {3}\, c_{1} -2 \textit {\_Z} \right )\right )-1\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 52

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

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