Internal problem ID [15230]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.2 Homogeneous differential equations with
constant coefficients. Exercises page 121
Problem number: 440.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }-8 y^{\prime }+5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(4*diff(y(x),x$2)-8*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{1} \sin \left (\frac {x}{2}\right )+c_{2} \cos \left (\frac {x}{2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 28
DSolve[4*y''[x]-8*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (c_2 \cos \left (\frac {x}{2}\right )+c_1 \sin \left (\frac {x}{2}\right )\right ) \]