71.1.13 problem 27 (page 32)

Internal problem ID [19189]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 27 (page 32)
Date solved : Thursday, October 02, 2025 at 03:42:42 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 21

ode:=(x+2*y(x)+1)*diff(y(x),x) = 2*x+4*y(x)+3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{2}-\frac {\operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {7}{2}-\frac {25 x}{2}}}{2}\right )}{5}-\frac {7}{10} \]

✓ Mathematica. Time used: 2.998 (sec). Leaf size: 43

ode=(x+2*y[x]+1)*D[y[x],x]==2*x+4*y[x]+3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.064 (sec). Leaf size: 63

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (x + 2*y(x) + 1)*Derivative(y(x), x) - 4*y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {x}{2} - \frac {W\left (- \frac {\sqrt {C_{1} e^{- 25 x}}}{10 e^{\frac {7}{2}}}\right )}{5} - \frac {7}{10}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {W\left (\frac {\sqrt {C_{1} e^{- 25 x}}}{10 e^{\frac {7}{2}}}\right )}{5} - \frac {7}{10}\right ] \]