82.12.30 problem Ex. 33

Internal problem ID [18795]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 33
Date solved : Tuesday, January 28, 2025 at 12:17:45 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve((3*y(x)+2*x+4)-(4*x+6*y(x)+5)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {3 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-\frac {44}{9}-\frac {49 x}{9}+\frac {49 c_{1}}{9}}}{9}\right )}{14}-\frac {22}{21}-\frac {2 x}{3} \]

✓ Solution by Mathematica

Time used: 4.036 (sec). Leaf size: 43

DSolve[(3*y[x]+2*x+4)-(4*x+6*y[x]+5)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{42} \left (-9 W\left (-e^{-\frac {49 x}{9}-1+c_1}\right )-28 x-44\right ) \\ y(x)\to -\frac {2}{21} (7 x+11) \\ \end{align*}