Internal problem ID [15224]
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: 434.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2, y^{\prime \prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=0,y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (1+x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 12
DSolve[{y'''[x]-3*y''[x]+3*y'[x]-y[x]==0,{y[0]==1,y'[0]==2,y''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x+1) \]