64.10.26 problem 26

Internal problem ID [13432]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 05:42:19 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-4\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+7*diff(y(x),x)+10*y(x)=0,y(0) = -4, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{-5 x}-6 \,{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[{D[y[x],{x,2}]+7*D[y[x],x]+10*y[x]==0,{y[0]==-4,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (2-6 e^{3 x}\right ) \]