83.26.15 problem 15

Internal problem ID [19268]
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 (C) at page 93
Problem number : 15
Date solved : Monday, March 31, 2025 at 07:03:52 PM
CAS classification : [[_3rd_order, _reducible, _mu_y2]]

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y&=x^{2}+\frac {1}{x^{2}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 44

ode:=x^3*diff(diff(diff(y(x),x),x),x)-3*x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)-8*y(x) = x^2+1/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {32 \ln \left (x \right )^{3} x^{4}+192 c_3 \,x^{4} \ln \left (x \right )^{2}+192 c_2 \,x^{4} \ln \left (x \right )+192 c_1 \,x^{4}-3}{192 x^{2}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 48

ode=x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]+7*x*D[y[x],x]-8*y[x]==x^2+1/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{64 x^2}+\frac {1}{6} x^2 \log ^3(x)+c_1 x^2+c_3 x^2 \log ^2(x)+c_2 x^2 \log (x) \]

✓ Sympy. Time used: 0.445 (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)) - x**2 + 7*x*Derivative(y(x), x) - 8*y(x) - 1/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {32 x^{4} \left (C_{1} + C_{2} \log {\left (x \right )} + C_{3} \log {\left (x \right )}^{2} + \log {\left (x \right )}^{3}\right ) - 3}{192 x^{2}} \]