80.8.11 problem 14

Internal problem ID [18590]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 12:03:23 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime }&=17 x^{6} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(x^4*diff(y(x),x$4)+x^3*diff(y(x),x$3)-20*x^2*diff(y(x),x$2)+20*x*diff(y(x),x)=17*x^6,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {612 \ln \left (x \right ) x^{9}+\left (1296 c_3 -323\right ) x^{9}+3888 c_{1} x^{5}+7776 c_4 \,x^{3}-2592 c_{2}}{7776 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 49

DSolve[x^4*D[y[x],{x,4}]+x^3*D[y[x],{x,3}]-20*x^2*D[y[x],{x,2}]+20*x*D[y[x],x]==17*x^6,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {17}{216} x^6 \log (x)+\left (-\frac {323}{7776}+\frac {c_3}{6}\right ) x^6-\frac {c_1}{3 x^3}+\frac {c_2 x^2}{2}+c_4 \]