60.1.214 problem 215

Internal problem ID [10228]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 215
Date solved : Monday, January 27, 2025 at 06:40:19 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.348 (sec). Leaf size: 61

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

\[ y = \frac {3}{2}+\frac {\sqrt {3}\, \left (3 x -1\right ) \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (3\right )-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (3 x -1\right )^{2}\right )+2 \sqrt {3}\, c_{1} +6 \textit {\_Z} \right )\right )}{6}-\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 80

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

\[ \text {Solve}\left [6 \sqrt {3} \arctan \left (\frac {4-3 y(x)}{\sqrt {3} (y(x)+2 x-2)}\right )=3 \log \left (\frac {3 x^2+3 y(x)^2+3 (x-3) y(x)-6 x+7}{(1-3 x)^2}\right )+6 \log (3 x-1)+2 c_1,y(x)\right ] \]