81.6.4 problem 4

Internal problem ID [18616]
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 : 4
Date solved : Monday, March 31, 2025 at 05:46:40 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

ode:=x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+4*y(x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x \right )}{4}+\frac {1}{4}+c_1 x +\frac {c_2}{x^{2}}+c_3 \,x^{2} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 30

ode=x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 x^2+\frac {c_1}{x^2}+\frac {1}{4} (\log (x)+1)+c_2 x \]

✓ Sympy. Time used: 0.285 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 2*x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 4*y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} + C_{2} x + C_{3} x^{2} + \frac {\log {\left (x \right )}}{4} + \frac {1}{4} \]