88.23.9 problem 10

Internal problem ID [24183]
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 5. Special Techniques for Linear Equations. Miscellaneous Exercises at page 162
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:00:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)-4*y(x) = 12*exp(2*x); 
ic:=[y(0) = 2, D(y)(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 12

ode=D[y[x],{x,2}]+3*D[y[x],x]-4*y[x]==12*Exp[2*x]; 
ic={y[0]==2,Derivative[1][y][0] ==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 12*exp(2*x) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 e^{2 x} \]