Internal problem ID [4739]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter IX, Special forms of differential equations. Examples XVII. page
247
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y n^{2}-\frac {6 y}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve(diff(y(x),x$2)+n^2*y(x)=6*y(x)/x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (c_{1} n^{2} x^{2}+3 c_{2} n x -3 c_{1} \right ) \cos \left (n x \right )+\sin \left (n x \right ) \left (c_{2} n^{2} x^{2}-3 c_{1} n x -3 c_{2} \right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 79
DSolve[y''[x]+n^2*y[x]==6*y[x]/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \sqrt {x} \left (\left (c_2 \left (-n^2\right ) x^2+3 c_1 n x+3 c_2\right ) \cos (n x)+\left (c_1 \left (n^2 x^2-3\right )+3 c_2 n x\right ) \sin (n x)\right )}{(n x)^{5/2}} \]