Internal problem ID [13263]
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: 17.1 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(4*diff(y(x),x$2)-y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-\frac {x}{2}}+c_{2} {\mathrm e}^{\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 22
DSolve[4*y''[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (c_1 e^x+c_2\right ) \]