Internal problem ID [11147]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 11.
Equations in which M and N are linear but not homogeneous. Page 16
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 y+\left (x +y+1\right ) y^{\prime }=-4 x -1} \]
✓ Solution by Maple
Time used: 0.516 (sec). Leaf size: 29
dsolve((4*x+3*y(x)+1)+(x+y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -3-\frac {\left (x -2\right ) \left (2 \operatorname {LambertW}\left (c_{1} \left (x -2\right )\right )+1\right )}{\operatorname {LambertW}\left (c_{1} \left (x -2\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.385 (sec). Leaf size: 159
DSolve[(4*x+3*y[x]+1)+(x+y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+(2 x-1) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{y(x)+x+1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+y(x) \left (\log \left (-\frac {3 (-2)^{2/3} (x-2)}{y(x)+x+1}\right )-\log \left (\frac {3 (-2)^{2/3} (y(x)+2 x-1)}{y(x)+x+1}\right )+1\right )+x+1\right )}{9 (y(x)+2 x-1)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ] \]