63.1.32 problem 49

Internal problem ID [15472]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 49
Date solved : Thursday, October 02, 2025 at 10:16:51 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 20

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

\[ y = -\frac {x}{2}+\frac {\operatorname {LambertW}\left (c_1 \,{\mathrm e}^{5+8 x}\right )}{8}-\frac {5}{8} \]

✓ Mathematica. Time used: 2.376 (sec). Leaf size: 39

ode=(x+2*y[x]+1)-(2*x+4*y[x]+3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.686 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = - \frac {x}{2} + \frac {W\left (C_{1} e^{8 x + 5}\right )}{8} - \frac {5}{8} \]