86.10.13 problem 13

Internal problem ID [23193]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 9. The operational method. Exercise 9b at page 134
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:24:13 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=5 x^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 5*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{x}+5 x^{3}+30 x^{2}+90 x +120 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to 5 \left (x^3+6 x^2+18 x+24\right )+c_1 e^x+c_2 e^x x \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = 5 x^{3} + 30 x^{2} + 90 x + \left (C_{1} + C_{2} x\right ) e^{x} + 120 \]