15.3.3 problem 3

Internal problem ID [2896]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:27:49 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.172 (sec). Leaf size: 51

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

\[ y = \frac {1}{3}+\frac {\tan \left (\operatorname {RootOf}\left (\sqrt {2}\, \ln \left (2\right )+\sqrt {2}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (3 x +1\right )^{2}\right )+2 \sqrt {2}\, c_1 -2 \textit {\_Z} \right )\right ) \sqrt {2}\, \left (-3 x -1\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 77

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

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