Internal problem ID [13233]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.3 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-20 y=27 x^{5}} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{5} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve([x^2*diff(y(x),x$2)-20*y(x)=27*x^5,x^5],y(x), singsol=all)
\[ y = \frac {c_{2}}{x^{4}}+c_{1} x^{5}+x^{5} \left (-\frac {1}{3}+3 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 29
DSolve[x^2*y''[x]-20*y[x]==27*x^5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^5 \log (x)+\left (-\frac {1}{3}+c_2\right ) x^5+\frac {c_1}{x^4} \]