12.8.4 problem 3c

Internal problem ID [1740]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 3c
Date solved : Monday, January 27, 2025 at 05:34:01 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0) = 7, D(y)(0) = 4],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (7-3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]+y[x]==0,{y[0]==7,Derivative[1][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (7-3 x) \]