Internal problem ID [3839]
Book: Differential and integral calculus, vol II By N. Piskunov. 1974
Section: Chapter 1
Problem number: Example, page 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x +y-1}{4 x +2 y+5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 35
dsolve(diff(y(x),x)=(2*x+y(x)-1)/(4*x+2*y(x)+5),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\LambertW \left (\frac {2 \,{\mathrm e}^{\frac {18}{7}} {\mathrm e}^{\frac {25 x}{7}} {\mathrm e}^{-\frac {25 c_{1}}{7}}}{7}\right )+\frac {18}{7}+\frac {25 x}{7}-\frac {25 c_{1}}{7}}}{5}-\frac {9}{5}-2 x \]
✓ Solution by Mathematica
Time used: 60.02 (sec). Leaf size: 30
DSolve[y'[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} \text {ProductLog}\left (-e^{\frac {25 x}{7}-1+c_1}\right )-2 x-\frac {9}{5} \\ \end{align*}