56.3.6 problem 6

Internal problem ID [8864]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:07:40 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 (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 18

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

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