Internal problem ID [3749]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 495.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (1+x +9 y\right ) y^{\prime }+5 y=-x -1} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 29
dsolve((1+x+9*y(x))*diff(y(x),x)+1+x+5*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x +1\right ) \left (2+3 \operatorname {LambertW}\left (\frac {2 c_{1} \left (x +1\right )}{3}\right )\right )}{9 \operatorname {LambertW}\left (\frac {2 c_{1} \left (x +1\right )}{3}\right )} \]
✓ Solution by Mathematica
Time used: 1.908 (sec). Leaf size: 145
DSolve[(1+x+9 y[x])y'[x]+1+x+5 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {(-2)^{2/3} \left ((x+1) \left (3 \log \left (-\frac {6 (-2)^{2/3} (x+1)}{9 y(x)+x+1}\right )-3 \log \left (\frac {9 (-2)^{2/3} (3 y(x)+x+1)}{9 y(x)+x+1}\right )+1\right )+9 y(x) \left (\log \left (-\frac {6 (-2)^{2/3} (x+1)}{9 y(x)+x+1}\right )-\log \left (\frac {9 (-2)^{2/3} (3 y(x)+x+1)}{9 y(x)+x+1}\right )+1\right )\right )}{27 (3 y(x)+x+1)}=\frac {1}{9} (-2)^{2/3} \log (x+1)+c_1,y(x)\right ] \]