2.1152   ODE No. 1152

\[ \left (a^2 x^2-6\right ) y(x)+x^2 y''(x)=0 \]

✓ Mathematica : cpu = 0.012177 (sec), leaf count = 114

DSolve[(-6 + a^2*x^2)*y[x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {\sqrt {\frac {2}{\pi }} c_1 \sqrt {x} \left (\frac {3 \sin (a x)}{a^2 x^2}-\sin (a x)-\frac {3 \cos (a x)}{a x}\right )}{\sqrt {a x}}+\frac {\sqrt {\frac {2}{\pi }} c_2 \sqrt {x} \left (-\frac {3 \cos (a x)}{a^2 x^2}-\frac {3 \sin (a x)}{a x}+\cos (a x)\right )}{\sqrt {a x}}\right \}\right \}\]

✓ Maple : cpu = 0.284 (sec), leaf count = 53

dsolve(x^2*diff(diff(y(x),x),x)+(a^2*x^2-6)*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {\left (a^{2} c_{1} x^{2}+3 a c_{2} x -3 c_{1} \right ) \cos \left (a x \right )+\sin \left (a x \right ) \left (a^{2} c_{2} x^{2}-3 a c_{1} x -3 c_{2} \right )}{x^{2}}\]