Internal problem ID [14738]
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: 29.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y=\frac {1}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)-11*x*diff(y(x),x)+16*y(x)=1/x^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {25 c_{3} \ln \left (x \right ) x^{6}+25 c_{1} x^{6}+25 c_{2} +x}{25 x^{4}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 33
DSolve[x^3*y'''[x]+3*x^2*y''[x]-11*x*y'[x]+16*y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^4}+\frac {1}{25 x^3}+c_2 x^2+c_3 x^2 \log (x) \]