56.3.7 problem 7

Internal problem ID [8865]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:07:44 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 \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 35

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

\[ y(x)\to \frac {1}{2} ((1-\tan (1)+2 c_1 \tan (1)) \sin (x)-(x-2 c_1) \cos (x)) \]