75.5.14 problem 113

Internal problem ID [16679]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 113
Date solved : Monday, March 31, 2025 at 03:05:12 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 41

ode:=8*x+4*y(x)+1+(4*x+2*y(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -2 x -\frac {1}{2}-\frac {\sqrt {-4 c_1 +4 x +1}}{2} \\ y &= -2 x -\frac {1}{2}+\frac {\sqrt {-4 c_1 +4 x +1}}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.107 (sec). Leaf size: 55

ode=(8*x+4*y[x]+1)+(4*x+2*y[x]+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-4 x-\sqrt {4 x+1+4 c_1}-1\right ) \\ y(x)\to \frac {1}{2} \left (-4 x+\sqrt {4 x+1+4 c_1}-1\right ) \\ \end{align*}

✓ Sympy. Time used: 0.988 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x + (4*x + 2*y(x) + 1)*Derivative(y(x), x) + 4*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 2 x - \frac {\sqrt {C_{1} + 4 x}}{2} - \frac {1}{2}, \ y{\left (x \right )} = - 2 x + \frac {\sqrt {C_{1} + 4 x}}{2} - \frac {1}{2}\right ] \]