15.16.14 problem 14

Internal problem ID [3234]
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
Date solved : Monday, January 27, 2025 at 07:27:12 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y&=\frac {4}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y = \frac {9 c_3 \,x^{\frac {7}{3}+\frac {\sqrt {31}}{3}}+9 c_2 \,x^{\frac {7}{3}-\frac {\sqrt {31}}{3}}+9 c_{1} x^{3}-2}{9 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 51

DSolve[3*x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]-10*x*D[y[x],x]+10*y[x]==4/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{\frac {1}{3} \left (1+\sqrt {31}\right )}+c_1 x^{\frac {1}{3}-\frac {\sqrt {31}}{3}}-\frac {2}{9 x^2}+c_3 x \]