64.10.42 problem 42

Internal problem ID [13448]
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 : 42
Date solved : Tuesday, January 28, 2025 at 05:42:52 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 21

dsolve([diff(y(x),x$3)-5*diff(y(x),x$2)+9*diff(y(x),x)-5*y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 6],y(x), singsol=all)
 

\[ y = \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) {\mathrm e}^{2 x}+{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 25

DSolve[{D[y[x],{x,3}]-5*D[y[x],{x,2}]+9*D[y[x],x]-5*y[x]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (2 e^x \sin (x)-e^x \cos (x)+1\right ) \]