Internal problem ID [10174]
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 19. Summary.
Page 29
Problem number: Ex 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve((2*x+3*y(x)-1)+(2*x+3*y(x)-5)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 x}{3}-4 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x}{12}} c_{1} {\mathrm e}^{-\frac {7}{12}}}{12}\right )-\frac {7}{3} \]
✓ Solution by Mathematica
Time used: 3.74 (sec). Leaf size: 43
DSolve[(2*x+3*y[x]-1)+(2*x+3*y[x]-5)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -4 W\left (-e^{\frac {x}{12}-1+c_1}\right )-\frac {2 x}{3}-\frac {7}{3} \\ y(x)\to \frac {1}{3} (-2 x-7) \\ \end{align*}