83.15.3 problem 3

Internal problem ID [19109]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (G) at page 45
Problem number : 3
Date solved : Thursday, March 13, 2025 at 01:41:51 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=x^{2}+1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-6*diff(y(x),x) = x^2+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}-\frac {1}{2} x^{2}+\frac {25}{6} x -18 c_3 \right ) {\mathrm e}^{2 x}-6 c_{2} {\mathrm e}^{5 x}+9 c_{1} \right )}{18} \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 48

ode=D[y[x],{x,3}]-D[y[x],{x,2}]-6*D[y[x],x]==1+x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{108} \left (-6 x^3+3 x^2-25 x+18 \left (-3 c_1 e^{-2 x}+2 c_2 e^{3 x}+6 c_3\right )\right ) \]

✓ Sympy. Time used: 0.209 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - 6*Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 2 x} + C_{3} e^{3 x} - \frac {x^{3}}{18} + \frac {x^{2}}{36} - \frac {25 x}{108} \]