Internal problem ID [7432]
Book: Second order enumerated odes
Section: section 1
Problem number: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-x +2 c_{1} \right ) \cos \left (x \right )}{2}+\frac {\sin \left (x \right ) \left (2 c_{2} +1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x}{2}+c_1\right ) \cos (x)+c_2 \sin (x) \]