81.6.1 problem 1

Internal problem ID [18605]
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 : 1
Date solved : Thursday, March 13, 2025 at 12:25:04 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime }&=\ln \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=x^3*diff(diff(diff(y(x),x),x),x)+7*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x) = ln(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\ln \left (x \right )^{3}}{9}-\frac {4 \ln \left (x \right )^{2}}{9}-\frac {c_{2}}{x}+\frac {26 \ln \left (x \right )}{27}-\frac {c_{1}}{3 x^{3}}+c_3 \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 46

ode=x^3*D[y[x],{x,3}]+7*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]==(Log[x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {c_1}{3 x^3}+\frac {\log ^3(x)}{9}-\frac {4 \log ^2(x)}{9}+\frac {26 \log (x)}{27}-\frac {c_2}{x}+c_3 \]

✓ Sympy. Time used: 0.328 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 7*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) - log(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x^{3}} + \frac {C_{3}}{x} + \frac {\log {\left (x \right )}^{3}}{9} - \frac {4 \log {\left (x \right )}^{2}}{9} + \frac {26 \log {\left (x \right )}}{27} \]