71.10.13 problem 18

Internal problem ID [14508]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 06:42:47 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(y(x),x$4)-(3+I)*diff(y(x),x$3)+(4+3*I)*diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\left (2-i\right ) x}+c_{2} {\mathrm e}^{\left (1+2 i\right ) x}+c_{3} +c_4 x \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 46

DSolve[D[y[x],{x,4}]-(3+I)*D[y[x],{x,3}]+(4+3*I)*D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (-\frac {3}{25}-\frac {4 i}{25}\right ) c_1 e^{(1+2 i) x}+\left (\frac {3}{25}+\frac {4 i}{25}\right ) c_2 e^{(2-i) x}+c_4 x+c_3 \]