83.4.17 problem 17

Internal problem ID [19018]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 17
Date solved : Monday, March 31, 2025 at 06:33:10 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 20

ode:=(2*x+4*y(x)+3)*diff(y(x),x) = 2*y(x)+x+1; 
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: 4.092 (sec). Leaf size: 39

ode=(2*x+4*y[x]+3)*D[y[x],x]==(2*y[x]+x+1); 
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: 1.069 (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)
 

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