69.7.17 problem 192

Internal problem ID [18097]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 192
Date solved : Thursday, October 02, 2025 at 02:42:04 PM
CAS classification : [_linear]

\begin{align*} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=2*x^2*y(x)+2*y(x)+5+(2*x^3+2*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\frac {5 \arctan \left (x \right )}{2}+c_1}{x} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 31

ode=( 2*x^2*y[x]+2*y[x]+5)+(2*x^3+2*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\int _1^x-\frac {5}{2 \left (K[1]^2+1\right )}dK[1]+c_1}{x} \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*y(x) + (2*x**3 + 2*x)*Derivative(y(x), x) + 2*y(x) + 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {5 i \log {\left (x - i \right )}}{4} - \frac {5 i \log {\left (x + i \right )}}{4}}{x} \]