83.24.5 problem 5

Internal problem ID [19248]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (A) at page 81
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:03:14 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=\ln \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

ode:=x^3*diff(diff(diff(y(x),x),x),x)-3*x^2*diff(diff(y(x),x),x)+6*x*diff(y(x),x)-6*y(x) = ln(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\ln \left (x \right )^{2}}{6}-\frac {11 \ln \left (x \right )}{18}-\frac {85}{108}+c_3 \,x^{3}+c_2 \,x^{2}+c_1 x \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 38

ode=x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]+6*x*D[y[x],x]-6*y[x]==(Log[x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 x^3+c_2 x^2+\frac {1}{108} \left (-18 \log ^2(x)-66 \log (x)-85\right )+c_1 x \]

✓ Sympy. Time used: 0.283 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 3*x**2*Derivative(y(x), (x, 2)) + 6*x*Derivative(y(x), x) - 6*y(x) - log(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{2} + C_{3} x^{3} - \frac {\log {\left (x \right )}^{2}}{6} - \frac {11 \log {\left (x \right )}}{18} - \frac {85}{108} \]