8.7.10 problem 10

Internal problem ID [816]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 10
Date solved : Monday, January 27, 2025 at 03:09:12 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=13 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=0,y(0) = 3, D(y)(0) = 13],y(x), singsol=all)
 

\[ y = {\mathrm e}^{5 x} \left (3-2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 16

DSolve[{D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==0,{y[0]==3,Derivative[1][y][0] ==13}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{5 x} (3-2 x) \]