35.7.14 problem 17

Internal problem ID [6196]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 17
Date solved : Monday, January 27, 2025 at 01:47:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=8 x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-16*y(x)=8*x^4,y(x), singsol=all)
 

\[ y = \frac {8 x^{8} \ln \left (x \right )+\left (8 c_{2} -1\right ) x^{8}+8 c_{1}}{8 x^{4}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 28

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-16*y[x]==8*x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^4 \log (x)+\left (-\frac {1}{8}+c_2\right ) x^4+\frac {c_1}{x^4} \]