Internal problem ID [159]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 3, D(y)(0) = 8],y(x), singsol=all)
\[ y \relax (x ) = 4 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[x]+4*y[x]==0,{y[0]==3,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 4 \sin (2 x)+3 \cos (2 x) \\ \end{align*}