23.5.38 problem 38

Internal problem ID [6647]
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 : 38
Date solved : Tuesday, September 30, 2025 at 03:50:30 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 40

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

\[ y = \frac {\left (5+4 x -16 c_1 \right ) {\mathrm e}^{-x}}{16}-\frac {x^{3}}{3}+\frac {2 x^{2}}{3}+\frac {{\mathrm e}^{3 x} c_2}{3}-\frac {14 x}{9}+c_3 \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 54

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

\begin{align*} y(x)&\to \frac {1}{9} \left (-3 x^3+6 x^2-14 x+\frac {9}{16} e^{-x} (4 x+5-16 c_1)+3 c_2 e^{3 x}+9 c_3\right ) \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} + C_{3} e^{3 x} - \frac {x^{3}}{3} + \frac {2 x^{2}}{3} - \frac {14 x}{9} + \left (C_{2} + \frac {x}{4}\right ) e^{- x} \]