47.4.21 problem 23

Internal problem ID [9795]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 06:41:50 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime }-x^{2} y^{\prime }&=-x^{2}+3 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {c_1 \,x^{2}}{2}+\frac {1}{x}+x +c_2 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {c_1 x^2}{2}+x+\frac {1}{x}+c_2 \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 14

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

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