56.3.5 problem 5

Internal problem ID [8863]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:07:36 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^{\prime }\left (0\right )&=1\\ y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{2} (3 \sin (x)-x \cos (x)) \]