64.10.41 problem 41

Internal problem ID [13447]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 05:42:51 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-8\\ y^{\prime \prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 22

dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)+4*y(x)=0,y(0) = 1, D(y)(0) = -8, (D@@2)(y)(0) = -4],y(x), singsol=all)
 

\[ y = \frac {\left (6 x -23\right ) {\mathrm e}^{2 x}}{9}+\frac {32 \,{\mathrm e}^{-x}}{9} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 27

DSolve[{D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*y[x]==0,{y[0]==1,Derivative[1][y][0] ==-8,Derivative[2][y][0] ==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} e^{-x} \left (e^{3 x} (6 x-23)+32\right ) \]