15.8.35 problem 37

Internal problem ID [3038]
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 : 37
Date solved : Monday, January 27, 2025 at 07:11:03 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.277 (sec). Leaf size: 52

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

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

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 78

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

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