49.21.14 problem 5(b)

Internal problem ID [7744]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 5(b)
Date solved : Monday, January 27, 2025 at 03:11:50 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x +3 y+1}{x -2 y-1} \end{align*}

✓ Solution by Maple

Time used: 0.217 (sec). Leaf size: 61

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

\[ y = -\frac {5}{14}-\frac {x}{2}+\frac {\sqrt {3}\, \left (7 x -1\right ) \tan \left (\operatorname {RootOf}\left (-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (3\right )+\sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (7 x -1\right )^{2}\right )+2 \sqrt {3}\, c_{1} -4 \textit {\_Z} \right )\right )}{14} \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 85

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

\[ \text {Solve}\left [32 \sqrt {3} \arctan \left (\frac {4 y(x)+5 x+1}{\sqrt {3} (-2 y(x)+x-1)}\right )=3 \left (8 \log \left (\frac {4 \left (7 x^2+7 y(x)^2+(7 x+5) y(x)+x+1\right )}{(1-7 x)^2}\right )+16 \log (7 x-1)+7 c_1\right ),y(x)\right ] \]