71.1.16 problem 30

Internal problem ID [14325]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 06:26:39 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(diff(y(x),x$3)-7*diff(y(x),x$2)+12*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +{\mathrm e}^{3 x} c_{2} +c_{3} {\mathrm e}^{4 x} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]-7*D[y[x],{x,2}]+12*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} c_1 e^{3 x}+\frac {1}{4} c_2 e^{4 x}+c_3 \]