Internal problem ID [4852]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -16 y=8 x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-16*y(x)=8*x^4,y(x), singsol=all)
\[ y \left (x \right ) = x^{4} c_{2} +\frac {c_{1}}{x^{4}}+x^{4} \left (-\frac {1}{8}+\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 28
DSolve[x^2*y''[x]+x*y'[x]-16*y[x]==8*x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^4 \log (x)+\left (-\frac {1}{8}+c_2\right ) x^4+\frac {c_1}{x^4} \]