74.15.20 problem 20

Internal problem ID [16459]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 09:08:23 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(x^3*diff(y(x),x$4)+6*x^2*diff(y(x),x$3)+7*x*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_4 \ln \left (x \right )^{3}+c_{3} \ln \left (x \right )^{2}+\ln \left (x \right ) c_{2} +c_{1} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 33

DSolve[x^3*D[y[x],{x,4}]+6*x^2*D[y[x],{x,3}]+7*x*D[y[x],{x,2}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} c_3 \log ^3(x)+\frac {1}{2} c_2 \log ^2(x)+c_1 \log (x)+c_4 \]