50.8.20 problem 4(d)

Internal problem ID [7936]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 4(d)
Date solved : Sunday, March 30, 2025 at 12:38:38 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-3 y^{\prime }&=5 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=x*diff(diff(y(x),x),x)-3*diff(y(x),x) = 5*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_1 \,x^{2}-5\right )^{2}}{16 c_1}+c_2 \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 24

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

\[ y(x)\to \frac {c_1 x^4}{4}-\frac {5 x^2}{4}+c_2 \]

✓ Sympy. Time used: 0.281 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{4} - \frac {5 x^{2}}{4} \]