39.4.4 problem Problem 12.12

Internal problem ID [6538]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.12
Date solved : Sunday, March 30, 2025 at 11:06:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=diff(diff(y(x),x),x)-60*diff(y(x),x)-900*y(x) = 5*exp(10*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{30 \left (1+\sqrt {2}\right ) x} c_2 +{\mathrm e}^{-30 \left (\sqrt {2}-1\right ) x} c_1 -\frac {{\mathrm e}^{10 x}}{280} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 45

ode=D[y[x],{x,2}]-60*D[y[x],x]-900*y[x]==5*Exp[10*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {e^{10 x}}{280}+c_1 e^{-30 \left (\sqrt {2}-1\right ) x}+c_2 e^{30 \left (1+\sqrt {2}\right ) x} \]

✓ Sympy. Time used: 0.227 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-900*y(x) - 5*exp(10*x) - 60*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{30 x \left (1 - \sqrt {2}\right )} + C_{2} e^{30 x \left (1 + \sqrt {2}\right )} - \frac {e^{10 x}}{280} \]