Internal problem ID [13615]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 17. Second order Homogeneous equations with constant coefficients. Additional
exercises page 334
Problem number: 17.7 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)-diff(y(x),x)+(1/4+4*Pi^2)*y(x)=0,y(0) = 1, D(y)(0) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{2}} \cos \left (2 \pi x \right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 18
DSolve[{y''[x]-y'[x]+(1/4+4*Pi^2)*y[x]==0,{y[0]==1,y'[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x/2} \cos (2 \pi x) \]