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]]
\[ \boxed {2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = -\frac {7}{2}+\frac {{\mathrm e}^{2 x}}{2}+4 \,{\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.351 (sec). Leaf size: 70
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]
\[ y(x)\to \frac {1}{66} e^{-\frac {1}{4} \left (\sqrt {33}-3\right ) x} \left (\left (99-13 \sqrt {33}\right ) e^{\frac {\sqrt {33} x}{2}}-132 e^{\frac {1}{4} \left (\sqrt {33}-3\right ) x}+99+13 \sqrt {33}\right ) \]