33.5.4 problem Problem 24.26

Internal problem ID [7833]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.26
Date solved : Tuesday, September 30, 2025 at 05:06:08 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.093 (sec). Leaf size: 6

ode:=diff(diff(y(x),x),x)-y(x) = 0; 
ic:=[y(0) = 1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 108

ode=D[y[x],{x,2}]-y[x]==Sin[x]; 
ic={y[0]==1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (-e^{2 x} \int _1^0\frac {1}{2} e^{-K[1]} \sin (K[1])dK[1]+e^{2 x} \int _1^x\frac {1}{2} e^{-K[1]} \sin (K[1])dK[1]+\int _1^x-\frac {1}{2} e^{K[2]} \sin (K[2])dK[2]-\int _1^0-\frac {1}{2} e^{K[2]} \sin (K[2])dK[2]+e^{2 x}\right ) \end{align*}

✓ Sympy. Time used: 0.032 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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