Internal problem ID [7193]
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]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(x),x$2)+y(x)=sin(x),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (x \right ) \left (2 c_{2} +1\right )}{2}-\frac {\cos \left (x \right ) \left (x -2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 20
DSolve[{y''[x]+y[x]==Sin[x],{y[0] == 1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} x \cos (x)+\cos (x)+c_2 \sin (x) \]