30.1.3 problem Example, page 28

Internal problem ID [5691]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : Example, page 28
Date solved : Monday, January 27, 2025 at 01:07:19 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 23

dsolve(diff(y(x),x)=(2*x+y(x)-1)/(4*x+2*y(x)+5),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {7 \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {18}{7}+\frac {25 x}{7}-\frac {25 c_{1}}{7}}}{7}\right )}{10}-\frac {9}{5}-2 x \]

✓ Solution by Mathematica

Time used: 3.757 (sec). Leaf size: 41

DSolve[D[y[x],x]==(2*x+y[x]-1)/(4*x+2*y[x]+5),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {7}{10} W\left (-e^{\frac {25 x}{7}-1+c_1}\right )-2 x-\frac {9}{5} \\ y(x)\to -2 x-\frac {9}{5} \\ \end{align*}