29.18.19 problem 495

Internal problem ID [5093]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 495
Date solved : Monday, January 27, 2025 at 10:10:35 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.575 (sec). Leaf size: 29

dsolve((1+x+9*y(x))*diff(y(x),x)+1+x+5*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\left (x +1\right ) \left (2+3 \operatorname {LambertW}\left (\frac {2 \left (x +1\right ) c_{1}}{3}\right )\right )}{9 \operatorname {LambertW}\left (\frac {2 \left (x +1\right ) c_{1}}{3}\right )} \]

✓ Solution by Mathematica

Time used: 41.833 (sec). Leaf size: 145

DSolve[(1+x+9 y[x])D[y[x],x]+1+x+5 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {(-2)^{2/3} \left ((x+1) \left (3 \log \left (-\frac {6 (-2)^{2/3} (x+1)}{9 y(x)+x+1}\right )-3 \log \left (\frac {9 (-2)^{2/3} (3 y(x)+x+1)}{9 y(x)+x+1}\right )+1\right )+9 y(x) \left (\log \left (-\frac {6 (-2)^{2/3} (x+1)}{9 y(x)+x+1}\right )-\log \left (\frac {9 (-2)^{2/3} (3 y(x)+x+1)}{9 y(x)+x+1}\right )+1\right )\right )}{27 (3 y(x)+x+1)}=\frac {1}{9} (-2)^{2/3} \log (x+1)+c_1,y(x)\right ] \]