Internal problem ID [13354]
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 (h).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 23
dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+7*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y = c_{1} x +\frac {c_{2}}{x}+c_{3} \sin \left (\ln \left (x \right )\right )+c_{4} \cos \left (\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[x^4*y''''[x]+6*x^3*y'''[x]+7*x^2*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x+\frac {c_3}{x}+c_2 \cos (\log (x))+c_4 \sin (\log (x)) \]