9.2.14 problem problem 26

Internal problem ID [948]
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
Date solved : Monday, January 27, 2025 at 03:22:36 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0 \end{align*}

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: 0.007 (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)
 

\[ y = \frac {24}{5}-\frac {9 \,{\mathrm e}^{-5 x}}{5}-5 \,{\mathrm e}^{-5 x} x \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 26

DSolve[{D[y[x],{x,3}]+10*D[y[x],{x,2}]+25*D[y[x],x]==0,{y[0]==3,Derivative[1][y][0] ==4,Derivative[2][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{-5 x} \left (-25 x+24 e^{5 x}-9\right ) \]