60.1.213 problem 214

Internal problem ID [10227]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 214
Date solved : Monday, January 27, 2025 at 06:40:14 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+x -1\right ) y^{\prime }-y+2 x +3&=0 \end{align*}

✓ Solution by Maple

Time used: 0.318 (sec). Leaf size: 51

dsolve((y(x)+x-1)*diff(y(x),x)-y(x)+2*x+3=0,y(x), singsol=all)
 

\[ y = \frac {5}{3}+\frac {\tan \left (\operatorname {RootOf}\left (\sqrt {2}\, \ln \left (2\right )+\sqrt {2}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (2+3 x \right )^{2}\right )+2 c_{1} \sqrt {2}-2 \textit {\_Z} \right )\right ) \sqrt {2}\, \left (-3 x -2\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 78

DSolve[(y[x]+x-1)*D[y[x],x]-y[x]+2*x+3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \sqrt {2} \arctan \left (\frac {-y(x)+2 x+3}{\sqrt {2} (y(x)+x-1)}\right )=2 \log \left (\frac {6 x^2+3 y(x)^2-10 y(x)+8 x+11}{(3 x+2)^2}\right )+4 \log (3 x+2)+3 c_1,y(x)\right ] \]