Internal problem ID [15242]
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: 452.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(2*diff(y(x),x$3)-3*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{\frac {x}{2}}+c_{3} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 25
DSolve[2*y'''[x]-3*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 c_1 e^{x/2}+c_2 e^x+c_3 \]