Internal problem ID [2263]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 25, page 112
Problem number: 14.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y=\frac {4}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(3*x^3*diff(y(x),x$3)+4*x^2*diff(y(x),x$2)-10*x*diff(y(x),x)+10*y(x)=4/x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {9 c_{3} x^{\frac {7}{3}+\frac {\sqrt {31}}{3}}+9 c_{2} x^{\frac {7}{3}-\frac {\sqrt {31}}{3}}+9 c_{1} x^{3}-2}{9 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 51
DSolve[3*x^3*y'''[x]+4*x^2*y''[x]-10*x*y'[x]+10*y[x]==4/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^{\frac {1}{3} \left (1+\sqrt {31}\right )}+c_1 x^{\frac {1}{3}-\frac {\sqrt {31}}{3}}-\frac {2}{9 x^2}+c_3 x \]