Internal problem ID [11349]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _fully, _exact, _linear]]
\[ \boxed {\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 y^{\prime } x +6 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
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)
\[ y \left (x \right ) = \frac {x^{2} c_{1}}{\left (x +1\right ) \left (x^{2}-x +1\right )}+\frac {x c_{2}}{\left (x +1\right ) \left (x^{2}-x +1\right )}+\frac {c_{3}}{\left (x +1\right ) \left (x^{2}-x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 31
DSolve[(1+x^3)*y'''[x]+9*x^2*y''[x]+18*x*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_3 x^2+2 c_2 x+2 c_1}{2 x^3+2} \]