77.26.13 problem 13

Internal problem ID [20622]
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 : 13
Date solved : Thursday, October 02, 2025 at 06:16:21 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y&=x^{2}+3 x -4 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=x^3*diff(diff(diff(y(x),x),x),x)+6*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)+2*y(x) = x^2+3*x-4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sin \left (\ln \left (x \right )\right ) c_3 +\cos \left (\ln \left (x \right )\right ) c_2 +\frac {x^{3}}{30}+\frac {3 x^{2}}{10}+c_1 -2 x}{x} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 42

ode=x^3*D[y[x],{x,3}]+6*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]+2*y[x]==x^2+3*x-4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^3+9 x^2-60 x+30 c_2 \cos (\log (x))+30 c_1 \sin (\log (x))+30 c_3}{30 x} \end{align*}

✓ Sympy. Time used: 0.397 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 6*x**2*Derivative(y(x), (x, 2)) - x**2 + 8*x*Derivative(y(x), x) - 3*x + 2*y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} \sin {\left (\log {\left (x \right )} \right )} + C_{3} \cos {\left (\log {\left (x \right )} \right )} + \frac {x \left (x^{2} + 9 x - 60\right )}{30}}{x} \]