23.5.53 problem 53

Internal problem ID [6662]
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 : 53
Date solved : Tuesday, September 30, 2025 at 03:50:37 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -2 y+5 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=-2*y(x)+5*diff(y(x),x)-4*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 35

ode=-2*y[x] + 5*D[y[x],x] - 4*D[y[x],{x,2}] + D[y[x],{x,3}] == x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.110 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 2*y(x) + 5*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{2 x} - \frac {x}{2} + \left (C_{1} + C_{2} x\right ) e^{x} - \frac {5}{4} \]