Internal problem ID [298]
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 26.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 4, y^{\prime \prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve([diff(y(x),x$3)+10*diff(y(x),x$2)+25*diff(y(x),x)=0,y(0) = 3, D(y)(0) = 4, (D@@2)(y)(0) = 5],y(x), singsol=all)
\[ y \left (x \right ) = \frac {24}{5}-\frac {9 \,{\mathrm e}^{-5 x}}{5}-5 \,{\mathrm e}^{-5 x} x \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 26
DSolve[{y'''[x]+10*y''[x]+25*y'[x]==0,{y[0]==3,y'[0]==4,y''[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} e^{-5 x} \left (-25 x+24 e^{5 x}-9\right ) \]