64.8.5 problem 8

Internal problem ID [13393]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:41:37 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 )&=1\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0) = 1, D(y)(0) = 4],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (3 x +1\right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 14

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

\[ y(x)\to e^x (3 x+1) \]