62.38.11 problem Ex 11

Internal problem ID [13022]
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
Date solved : Tuesday, January 28, 2025 at 04:49:28 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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)
 

\[ y = \left (\ln \left (x \right ) c_{3} +c_{2} \right ) \sqrt {x}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 28

DSolve[4*x^2*D[y[x],{x,3}]+8*x*D[y[x],{x,2}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} (c_2 \log (x)+2 c_1-2 c_2)+c_3 \]