Internal problem ID [305]
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 38.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 10, y^{\prime \prime }\relax (0) = 250] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(x),x$3)-5*diff(y(x),x$2)+100*diff(y(x),x)-500*y(x)=0,y(0) = 0, D(y)(0) = 10, (D@@2)(y)(0) = 250],y(x), singsol=all)
\[ y \relax (x ) = 2 \,{\mathrm e}^{5 x}-2 \cos \left (10 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{y'''[x]-5*y''[x]+100*y'[x]-500*y[x]==0,{y[0]==0,y'[0]==10,y''[0]==250}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \left (e^{5 x}-\cos (10 x)\right ) \\ \end{align*}