Internal problem ID [15223]
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: 433.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {3 y^{\prime \prime }-2 y^{\prime }-8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(3*diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {10 x}{3}}+c_{1} \right ) {\mathrm e}^{-\frac {4 x}{3}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 24
DSolve[3*y''[x]-2*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-4 x/3}+c_2 e^{2 x} \]