60.1.225 problem 226

Internal problem ID [10239]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 226
Date solved : Monday, January 27, 2025 at 06:40:57 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 21

dsolve((4*y(x)-2*x-3)*diff(y(x),x)+2*y(x)-x-1=0,y(x), singsol=all)
 

\[ y = \frac {x}{2}-\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{5+8 x}\right )}{8}+\frac {5}{8} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 41

DSolve[(4*y[x]-2*x-3)*D[y[x],x]+2*y[x]-x-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (-W\left (-e^{8 x-1+c_1}\right )+4 x+5\right ) \\ y(x)\to \frac {1}{8} (4 x+5) \\ \end{align*}