56.3.4 problem 4

Internal problem ID [8862]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:07:32 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 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 20

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

\[ y = \frac {\left (-x +2 c_{1} \right ) \cos \left (x \right )}{2}+\frac {3 \sin \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 23

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

\[ y(x)\to \frac {3 \sin (x)}{2}+\left (-\frac {x}{2}+c_1\right ) \cos (x) \]