88.15.1 problem 1

Internal problem ID [24097]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 97
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:59:12 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)-6*y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-6 x} c_2 +{\mathrm e}^{x} c_1 -\frac {x^{3}}{6}-\frac {5 x^{2}}{12}-\frac {31 x}{36}-\frac {185}{216} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 39

ode=D[y[x],{x,2}]+5*D[y[x],x]-6*y[x]==x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{216} \left (-36 x^3-90 x^2-186 x-185\right )+c_1 e^{-6 x}+c_2 e^x \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 - 6*y(x) + 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 6 x} + C_{2} e^{x} - \frac {x^{3}}{6} - \frac {5 x^{2}}{12} - \frac {31 x}{36} - \frac {185}{216} \]