Internal problem ID [11712]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 y+\left (x +y+1\right ) y^{\prime }=-4 x -1} \] With initial conditions \begin {align*} [y \left (3\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 39
dsolve([(4*x+3*y(x)+1)+(x+y(x)+1)*diff(y(x),x)=0,y(3) = -4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2 x \operatorname {LambertW}\left (-\left (x -2\right ) {\mathrm e}^{-1}\right )+\operatorname {LambertW}\left (-\left (x -2\right ) {\mathrm e}^{-1}\right )-x +2}{\operatorname {LambertW}\left (-\left (x -2\right ) {\mathrm e}^{-1}\right )} \]
✓ Solution by Mathematica
Time used: 65.902 (sec). Leaf size: 197
DSolve[{(4*x+3*y[x]+1)+(x+y[x]+1)*y'[x]==0,{y[-2]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+(2 x-1) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{y(x)+x+1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+y(x) \left (\log \left (-\frac {3 (-2)^{2/3} (x-2)}{y(x)+x+1}\right )-\log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+1\right )+x+1\right )}{9 (y(x)+2 x-1)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+\frac {1}{27} (-2)^{2/3} \left (-1-3 i \pi -3 \log (4)-3 \log \left (-9 (-2)^{2/3}\right )+3 \log \left (12 (-2)^{2/3}\right )\right ),y(x)\right ] \]