82.29.1 problem Ex. 1

Internal problem ID [18804]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 76
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 12:59:21 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

\[ y \left (x \right ) = \frac {x^{3}}{6}-\frac {3 x^{2}}{4}-c_{2} {\mathrm e}^{-x}+\frac {{\mathrm e}^{-2 x} c_{1}}{2}+\frac {7 x}{4}+c_3 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 47

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

\[ y(x)\to \frac {x^3}{6}-\frac {3 x^2}{4}+\frac {7 x}{4}-\frac {1}{2} c_1 e^{-2 x}-c_2 e^{-x}+c_3 \]

✓ Sympy. Time used: 0.233 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 2 x} + C_{3} e^{- x} + \frac {x^{3}}{6} - \frac {3 x^{2}}{4} + \frac {7 x}{4} \]