Internal problem ID [14728]
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: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^3*diff(y(x),x$3)+6*x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} +c_{2} \ln \left (x \right )+c_{3} \ln \left (x \right )^{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[x^3*y'''[x]+6*x^2*y''[x]+7*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_3 \log ^2(x)+c_2 \log (x)+c_1}{x} \]