Internal problem ID [1483]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {14}{5}}, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 10\right ] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
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)
\[ y \relax (x ) = \frac {\left (10 x +5\right ) {\mathrm e}^{-\frac {5 x}{3}} {\mathrm e}^{\frac {8 x}{3}}}{5}+\frac {9 \,{\mathrm e}^{-\frac {5 x}{3}}}{5} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[{3*y'''[x]-y''[x]-7*y'[x]+5*y[x]==0,{y[0]==14/5,y'[0]==0,y''[0]==10}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (2 x+1)+\frac {9}{5} e^{-5 x/3} \\ \end{align*}