Internal problem ID [296]
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 24.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1, y^{\prime \prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([2*diff(y(x),x$3)-3*diff(y(x),x$2)-2*diff(y(x),x)=0,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = -\frac {7}{2}+4 \,{\mathrm e}^{-\frac {x}{2}}+\frac {{\mathrm e}^{2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 50
DSolve[{2*y'''[x]-3*y''[x]-3*y'[x]==0,{y[0]==1,y'[0]==-1,y''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{33} e^{3 x/4} \left (99 \cosh \left (\frac {\sqrt {33} x}{4}\right )-13 \sqrt {33} \sinh \left (\frac {\sqrt {33} x}{4}\right )\right )-2 \\ \end{align*}