60.1.223 problem 224

Internal problem ID [10237]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 224
Date solved : Monday, January 27, 2025 at 06:40:53 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 23

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

\[ y = -\frac {2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{2}\right )}{5}+3 x -\frac {2}{5} \]

✓ Solution by Mathematica

Time used: 3.209 (sec). Leaf size: 40

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

\begin{align*} y(x)\to 3 x-\frac {2}{5} \left (1+W\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right ) \\ y(x)\to 3 x-\frac {2}{5} \\ \end{align*}