Internal problem ID [13616]
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 (b).
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: 0.016 (sec). Leaf size: 29
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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {x}{2}} \left (2 \pi \cos \left (2 \pi x \right )-\sin \left (2 \pi x \right )\right )}{2 \pi } \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 35
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]
\[ y(x)\to \frac {e^{x/2} (2 \pi \cos (2 \pi x)-\sin (2 \pi x))}{2 \pi } \]