81.7.8 problem 9

Internal problem ID [18634]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 9
Date solved : Monday, March 31, 2025 at 05:48:29 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {3 x^{2}}{8}-\frac {c_1}{2 x^{2}}+c_2 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 24

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

\[ y(x)\to \frac {3 x^2}{8}-\frac {c_1}{2 x^2}+c_2 \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x^{2}} + \frac {3 x^{2}}{8} \]