83.43.9 problem Ex 10 page 11

Internal problem ID [19446]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 10 page 11
Date solved : Monday, March 31, 2025 at 07:14:54 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 23

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

\[ y = \frac {\operatorname {LambertW}\left (2 \,{\mathrm e}^{-2+3 x -3 c_1}\right )}{2}-2 x +1 \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 67

ode=D[y[x],x]==(6*x-2*y[x]-7)/(2*x+3*y[x]-6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-\sqrt {22 x^2-66 x+9 (4+c_1)}-2 x+6\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {22 x^2-66 x+9 (4+c_1)}-2 x+6\right ) \\ \end{align*}

✓ Sympy. Time used: 0.968 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - 2 x + \frac {W\left (C_{1} e^{3 x - 2}\right )}{2} + 1 \]