28.2.68 problem 68

Internal problem ID [4511]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 68
Date solved : Sunday, March 30, 2025 at 03:24:50 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 9*x^2*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = x c_2 \ln \left (x \right )+c_3 x +\frac {12 x^{3} \ln \left (x \right )-28 x^{3}+c_1}{4 x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 31

ode=x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==9*x^2*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -7 x^2+c_2 x+\frac {c_1}{x}+x (3 x+c_3) \log (x) \]

✓ Sympy. Time used: 0.320 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 9*x**2*log(x) + 2*x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x^{2} \left (C_{2} + C_{3} \log {\left (x \right )} + 3 x \log {\left (x \right )} - 7 x\right )}{x} \]