89.5.1 problem 1

Internal problem ID [24351]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:21:34 PM
CAS classification : [_linear]

\begin{align*} x^{4}+2 y-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {x^4}{2}+c_1 x^2 \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 12

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

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