77.15.3 problem 3

Internal problem ID [20473]
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, October 02, 2025 at 06:03:13 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: 0.002 (sec). Leaf size: 33

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);
 

\[ y = \frac {x^{2}}{36}-\frac {x^{3}}{18}-\frac {{\mathrm e}^{-2 x} c_1}{2}+\frac {{\mathrm e}^{3 x} c_2}{3}-\frac {25 x}{108}+c_3 \]

✓ Mathematica. Time used: 0.032 (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]
 

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.132 (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)
 

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