86.7.13 problem 15

Internal problem ID [23160]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5c at page 83
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:23:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&={\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)-15*y(x) = exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-5 x} c_2 +{\mathrm e}^{3 x} c_1 +\frac {{\mathrm e}^{4 x}}{9} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 31

ode=D[y[x],{x,2}]+2*D[y[x],x]-15*y[x]==Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{4 x}}{9}+c_1 e^{-5 x}+c_2 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-15*y(x) - exp(4*x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{3 x} + \frac {e^{4 x}}{9} \]