12.18.19 problem section 9.2, problem 19

Internal problem ID [2133]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 19
Date solved : Monday, January 27, 2025 at 05:42:43 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {14}{5}}\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 21

dsolve([3*diff(y(x),x$3)-diff(y(x),x$2)-7*diff(y(x),x)+5*y(x)=0,y(0) = 14/5, D(y)(0) = 0, (D@@2)(y)(0) = 10],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {5 x}{3}} \left (\frac {9}{5}+\left (2 x +1\right ) {\mathrm e}^{\frac {8 x}{3}}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

DSolve[{3*D[y[x],{x,3}]-D[y[x],{x,2}]-7*D[y[x],x]+5*y[x]==0,{y[0]==14/5,Derivative[1][y][0] ==0,Derivative[2][y][0] ==10}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (2 x+1)+\frac {9}{5} e^{-5 x/3} \]