56.3.9 problem 9

Internal problem ID [8867]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:07:52 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 (1\right )&=0\\ y \left (2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.191 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{4} (\sec (1) \sin (x) (-\sin (1)+\sin (3)+\cos (1)+\cos (3))-2 \cos (x) (x-1+\sin (2)-\cos (2))) \]