8.9.10 problem 21

Internal problem ID [854]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 21
Date solved : Monday, January 27, 2025 at 03:10:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=11 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=0,y(0) = 7, D(y)(0) = 11],y(x), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{3 x}+5 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==0,{y[0]==7,Derivative[1][y][0] ==11}},y[x],x,IncludeSingularSolutions -> True]
 

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