23.5.48 problem 48

Internal problem ID [6657]
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 : 48
Date solved : Tuesday, September 30, 2025 at 03:50:35 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} -y+3 y^{\prime }-3 y^{\prime \prime }+y^{\prime \prime \prime }&=x \left (1-{\mathrm e}^{x} x^{2}\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 32

ode:=-y(x)+3*diff(y(x),x)-3*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = x*(1-exp(x)*x^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x^{6}+120 c_3 \,x^{2}+120 c_2 x +120 c_1 \right ) {\mathrm e}^{x}}{120}-x -3 \]

✓ Mathematica. Time used: 0.145 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to -\frac {1}{120} e^x x^6+c_3 e^x x^2+x \left (-1+c_2 e^x\right )+c_1 e^x-3 \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = - x + \left (C_{1} + x \left (C_{2} + x \left (C_{3} - \frac {x^{4}}{120}\right )\right )\right ) e^{x} - 3 \]