3.3 problem 3

Internal problem ID [6440]

Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 3.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}

Solution by Maple

Time used: 0.013 (sec). Leaf size: 20

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

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

Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 20

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

\begin{align*} y(x)\to -\frac {1}{2} x \cos (x)+\cos (x)+c_2 \sin (x) \\ \end{align*}