Internal problem ID [15238]
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: 448.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{x} \sin \left (x \right )+c_{3} {\mathrm e}^{x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 34
DSolve[y'''[x]-2*y''[x]+2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x ((c_2-c_1) \cos (x)+(c_1+c_2) \sin (x))+c_3 \]