7.8.11 problem 11

Internal problem ID [225]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 11
Date solved : Wednesday, February 05, 2025 at 03:18:14 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 12

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

\[ y(x)\to 5 e^x \sin (x) \]