Internal problem ID [9671]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1343.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {\left (x^{2} a \left (1-a \right )-b \left (x +b \right )\right ) y}{x^{4}}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 58
dsolve(diff(diff(y(x),x),x) = -(x^2*a*(1-a)-b*(x+b))/x^4*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {BesselI}\left (a +1, \frac {b}{x}\right ) c_{1} b -\operatorname {BesselK}\left (a +1, \frac {b}{x}\right ) c_{2} b +2 \left (a x +\frac {b}{2}\right ) \left (\operatorname {BesselI}\left (a , \frac {b}{x}\right ) c_{1} +c_{2} \operatorname {BesselK}\left (a , \frac {b}{x}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.275 (sec). Leaf size: 65
DSolve[y''[x] == -((((1 - a)*a*x^2 - b*(b + x))*y[x])/x^4),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 (2 a x+b) \operatorname {BesselI}\left (a,\frac {b}{x}\right )+b c_1 \operatorname {BesselI}\left (a+1,\frac {b}{x}\right )+c_2 \left ((2 a x+b) K_a\left (\frac {b}{x}\right )-b K_{a+1}\left (\frac {b}{x}\right )\right ) \]