73.12.14 problem 19.3 (b)

Internal problem ID [15366]
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)
Date solved : Tuesday, January 28, 2025 at 07:53:49 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end{align*}

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: 0.020 (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: 0.004 (sec). Leaf size: 21

DSolve[{D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==0,{y[0]==5,Derivative[1][y][0] ==13,Derivative[2][y][0] ==86}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (27 x^2+3 x+5\right ) \]