56.3.8 problem 8

Internal problem ID [8866]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:07:48 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 (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

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

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