Internal problem ID [14739]
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: 30.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y=\frac {1}{x^{13}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^3*diff(y(x),x$3)+16*x^2*diff(y(x),x$2)+70*x*diff(y(x),x)+80*y(x)=1/x^(13),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{648 x^{13}}+\frac {c_{1}}{x^{4}}+\frac {c_{2}}{x^{5}}+\frac {c_{3} \ln \left (x \right )}{x^{4}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 33
DSolve[x^3*y'''[x]+16*x^2*y''[x]+70*x*y'[x]+80*y[x]==1/x^(13),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{648 x^{13}}+\frac {c_1}{x^5}+\frac {c_2}{x^4}+\frac {c_3 \log (x)}{x^4} \]