Internal problem ID [3188]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 442.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (1+x +y\right ) y^{\prime }+1+4 x +3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.082 (sec). Leaf size: 29
dsolve((1+x+y(x))*diff(y(x),x)+1+4*x+3*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -3-\frac {\left (x -2\right ) \left (2 \LambertW \left (c_{1} \left (x -2\right )\right )+1\right )}{\LambertW \left (c_{1} \left (x -2\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.386 (sec). Leaf size: 159
DSolve[(1+x+y[x])y'[x]+1+4 x+3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+(2 x-1) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{y(x)+x+1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+y(x) \left (\log \left (-\frac {3 (-2)^{2/3} (x-2)}{y(x)+x+1}\right )-\log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+1\right )+x+1\right )}{9 (y(x)+2 x-1)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ] \]