73.10.4 problem 15.2 (d)

Internal problem ID [15299]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (d)
Date solved : Tuesday, January 28, 2025 at 07:51:50 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(0) = 1, D(y)(0) = 6],y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \left (4 x +1\right ) \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==0,{y[0]==1,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} (4 x+1) \]