21.1.7 problem 7

Internal problem ID [4083]
Book : Differential equations, Shepley L. Ross, 1964
Section : 2.4, page 55
Problem number : 7
Date solved : Monday, January 27, 2025 at 08:07:52 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 31

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

\[ y \left (x \right ) = -1-\tan \left (\operatorname {RootOf}\left (-4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 66

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

\[ \text {Solve}\left [32 \arctan \left (\frac {2 y(x)-x+3}{y(x)+2 x-1}\right )+8 \log \left (\frac {x^2+y(x)^2+2 y(x)-2 x+2}{5 (x-1)^2}\right )+16 \log (x-1)+5 c_1=0,y(x)\right ] \]