83.47.3 problem Ex 3 page 80

Internal problem ID [19501]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 3 page 80
Date solved : Thursday, March 13, 2025 at 02:42:56 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 36

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

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

✓ Sympy. Time used: 0.345 (sec). Leaf size: 29

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

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