15.8.22 problem 23

Internal problem ID [3025]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:09:15 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.287 (sec). Leaf size: 51

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

\[ y = \frac {1}{2}+\frac {\sqrt {3}\, \left (x +1\right ) \tan \left (\operatorname {RootOf}\left (-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (x +1\right )^{2}\right )+2 \sqrt {3}\, c_{1} +2 \textit {\_Z} \right )\right )}{6}-\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.100 (sec). Leaf size: 73

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

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