26.5.2 problem 3

Internal problem ID [4276]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 3
Date solved : Monday, January 27, 2025 at 08:47:25 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

dsolve((2*x+3*y(x)+1)+(2*y(x)-3*x+5)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 68

DSolve[(2*x+3*y[x]+1)+(2*y[x]-3*x+5)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [54 \arctan \left (\frac {3 y(x)+2 x+1}{2 y(x)-3 x+5}\right )+18 \log \left (\frac {4 \left (x^2+y(x)^2+2 y(x)-2 x+2\right )}{13 (x-1)^2}\right )+36 \log (x-1)+13 c_1=0,y(x)\right ] \]