56.3.3 problem 3

Internal problem ID [8861]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:07:28 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+y(x)=sin(x),y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right ) \left (2 c_{2} +1\right )}{2}-\frac {\cos \left (x \right ) \left (x -2\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 20

DSolve[{D[y[x],{x,2}]+y[x]==Sin[x],{y[0] == 1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} x \cos (x)+\cos (x)+c_2 \sin (x) \]