23.5.17 problem 17

Internal problem ID [6626]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 03:50:21 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 36

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

\[ y = c_2 \,{\mathrm e}^{-2 x}+\frac {\left (x^{4}-\frac {4}{3} x^{3}+\frac {4}{3} x^{2}+36 c_3 x +36 c_1 \right ) {\mathrm e}^{x}}{36} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 51

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

\begin{align*} y(x)&\to \frac {1}{972} e^x \left (27 x^4-36 x^3+36 x^2+12 (-2+81 c_3) x+8+972 c_2\right )+c_1 e^{-2 x} \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{3} e^{- 2 x} + \left (C_{1} + x \left (C_{2} + \frac {x^{3}}{36} - \frac {x^{2}}{27} + \frac {x}{27}\right )\right ) e^{x} \]