Internal problem ID [13351]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 20. Euler equations. Additional exercises page 382
Problem number: 20.4 (e).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+15*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sin \left (2 \ln \left (x \right )\right )+c_{2} \cos \left (2 \ln \left (x \right )\right )+c_{3} \sin \left (2 \ln \left (x \right )\right ) \ln \left (x \right )+c_{4} \cos \left (2 \ln \left (x \right )\right ) \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 34
DSolve[x^4*y''''[x]+6*x^3*y'''[x]+15*x^2*y''[x]+9*x*y'[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (c_2 \log (x)+c_1) \cos (2 \log (x))+(c_4 \log (x)+c_3) \sin (2 \log (x)) \]