77.5.14 problem 14

Internal problem ID [20394]
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 (D) at page 16
Problem number : 14
Date solved : Thursday, October 02, 2025 at 05:50:51 PM
CAS classification : [_linear]

\begin{align*} 1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=1+y(x)+x^2*y(x)+(x^3+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 16

ode=(1+y[x]+x^2*y[x])+(x+x^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-\arctan (x)+c_1}{x} \end{align*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*y(x) + (x**3 + x)*Derivative(y(x), x) + y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {i \log {\left (x - i \right )}}{2} - \frac {i \log {\left (x + i \right )}}{2}}{x} \]