62.38.4 problem Ex 4

Internal problem ID [13015]
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 4
Date solved : Tuesday, January 28, 2025 at 04:49:17 AM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve((1+x^3)*diff(y(x),x$3)+9*x^2*diff(y(x),x$2)+18*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{2}+c_{2} x +c_{3}}{\left (x +1\right ) \left (x^{2}-x +1\right )} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 31

DSolve[(1+x^3)*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]+18*x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_3 x^2+2 c_2 x+2 c_1}{2 x^3+2} \]