Internal problem ID [297]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 25.
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 }+2 y^{\prime \prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 15
dsolve([3*diff(y(x),x$3)+2*diff(y(x),x$2)=0,y(0) = -1, D(y)(0) = 0, (D@@2)(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {13}{4}+\frac {3 x}{2}+\frac {9 \,{\mathrm e}^{-\frac {2 x}{3}}}{4} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 23
DSolve[{3*y'''[x]+2*y''[x]==0,{y[0]==1,y'[0]==-1,y''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (14 x+27 e^{-2 x/3}-23\right ) \\ \end{align*}