23.2.11 problem 5

Internal problem ID [4128]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 5
Date solved : Monday, January 27, 2025 at 08:37:01 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 13

dsolve([diff(y(x),x$2)-6*diff(y(x),x)+5*y(x)=0,y(0) = 3, D(y)(0) = 7],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]-6*D[y[x],x]+5*y[x]==0,{y[0]==3,Derivative[1][y][0] ==7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (e^{4 x}+2\right ) \]