84.37.4 problem 26.4

Internal problem ID [22346]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 26. Solutions of linear differential equations with constant coefficients by Laplace transform. Solved problems. Page 159
Problem number : 26.4
Date solved : Thursday, October 02, 2025 at 08:37:49 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 19

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

\[ y = \frac {3 \,{\mathrm e}^{-x}}{2}-\frac {\cos \left (x \right )}{2}+\frac {\sin \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {1}{2} \left (3 e^{-x}+\sin (x)-\cos (x)\right ) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {\sin {\left (x \right )}}{2} - \frac {\cos {\left (x \right )}}{2} + \frac {3 e^{- x}}{2} \]