Internal problem ID [14729]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 20.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x^3*diff(y(x),x$4)+6*x^2*diff(y(x),x$3)+7*x*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{4} \ln \left (x \right )^{3}+c_{3} \ln \left (x \right )^{2}+c_{2} \ln \left (x \right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 33
DSolve[x^3*y''''[x]+6*x^2*y'''[x]+7*x*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} c_3 \log ^3(x)+\frac {1}{2} c_2 \log ^2(x)+c_1 \log (x)+c_4 \]