Internal problem ID [4742]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 47
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-25/4)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-3 \left (i x -\frac {1}{3} x^{2}+1\right ) c_{2} {\mathrm e}^{-i x}+3 \left (i x +\frac {1}{3} x^{2}-1\right ) c_{1} {\mathrm e}^{i x}}{x^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 59
DSolve[x^2*y''[x]+x*y'[x]+(x^2-25/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \left (\left (-c_2 x^2+3 c_1 x+3 c_2\right ) \cos (x)+\left (c_1 \left (x^2-3\right )+3 c_2 x\right ) \sin (x)\right )}{x^{5/2}} \]