44.1.34 problem 36

Internal problem ID [6909]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 36
Date solved : Monday, January 27, 2025 at 02:34:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \left (c_{2} {\mathrm e}^{\frac {9 x}{2}}+c_{1} \right ) {\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

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

\[ y(x)\to e^{-4 x} \left (c_1 e^{9 x/2}+c_2\right ) \]