Internal problem ID [10328]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62.
Summary. Page 144
Problem number: Ex 11.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(4*x^2*diff(y(x),x$3)+8*x*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} \sqrt {x}+c_{3} \sqrt {x}\, \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 28
DSolve[4*x^2*y'''[x]+8*x*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} (c_2 \log (x)+2 c_1-2 c_2)+c_3 \\ \end{align*}