74.15.29 problem 29

Internal problem ID [16468]
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
Date solved : Tuesday, January 28, 2025 at 09:08:45 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y&=\frac {1}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y = \frac {25 c_{3} \ln \left (x \right ) x^{6}+25 c_{1} x^{6}+25 c_{2} +x}{25 x^{4}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 33

DSolve[x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-11*x*D[y[x],x]+16*y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^4}+\frac {1}{25 x^3}+c_2 x^2+c_3 x^2 \log (x) \]