23.5.16 problem 16

Internal problem ID [6625]
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 : 16
Date solved : Tuesday, September 30, 2025 at 03:50:21 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 0.143 (sec). Leaf size: 20

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

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