75.6.6 problem 6

Internal problem ID [19974]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 6
Date solved : Thursday, October 02, 2025 at 05:04:38 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {x^2}{3}-\frac {c_1}{x}+c_2 \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 12

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

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