31.1.12 problem 4.1

Internal problem ID [5710]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 4.1
Date solved : Monday, January 27, 2025 at 01:11:01 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.615 (sec). Leaf size: 67

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

\[ y \left (x \right ) = \frac {\sqrt {15}\, \tan \left (\operatorname {RootOf}\left (\sqrt {15}\, \ln \left (5\right )-3 \sqrt {15}\, \ln \left (2\right )+\sqrt {15}\, \ln \left (3\right )+\sqrt {15}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (4 x +1\right )^{2}\right )+2 \sqrt {15}\, c_{1} -2 \textit {\_Z} \right )\right ) \left (-4 x -1\right )}{16}+\frac {x}{4}+\frac {9}{16} \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 85

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

\[ \text {Solve}\left [2 \sqrt {15} \arctan \left (\frac {-2 y(x)+8 x+3}{\sqrt {15} (2 y(x)-1)}\right )=15 \left (\log \left (\frac {2 \left (8 x^2+8 y(x)^2-(4 x+9) y(x)+6 x+3\right )}{(4 x+1)^2}\right )+2 \log (4 x+1)+8 c_1\right ),y(x)\right ] \]