Internal problem ID [13310]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients.
Additional exercises page 369
Problem number: 19.3 (b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 13, y^{\prime \prime }\left (0\right ) = 86] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=0,y(0) = 5, D(y)(0) = 13, (D@@2)(y)(0) = 86],y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \left (27 x^{2}+3 x +5\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{y'''[x]-6*y''[x]+12*y'[x]-8*y[x]==0,{y[0]==5,y'[0]==13,y''[0]==86}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (27 x^2+3 x+5\right ) \]