29.12.17 problem 336

Internal problem ID [4936]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 336
Date solved : Tuesday, March 04, 2025 at 07:32:04 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y \left (x \right ) = 2 x -3+\frac {c_{1}}{\sqrt {x^{2}+x +1}} \]

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 23

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

\[ y(x)\to \frac {c_1}{\sqrt {x^2+x+1}}+2 x-3 \]

✓ Sympy. Time used: 1.747 (sec). Leaf size: 19

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

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