29.18.11 problem 487

Internal problem ID [5085]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 487
Date solved : Monday, January 27, 2025 at 10:08:38 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} 4 \left (1-x -y\right ) y^{\prime }+2-x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.559 (sec). Leaf size: 28

dsolve(4*(1-x-y(x))*diff(y(x),x)+2-x = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.679 (sec). Leaf size: 109

DSolve[4(1-x-y[x])D[y[x],x]+2-x==0,y[x],x,IncludeSingularSolutions -> True]
 

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