60.3.181 problem 1185

Internal problem ID [11191]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1185
Date solved : Monday, January 27, 2025 at 10:48:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }-\left (2 x^{3}-4\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-(2*x^3-4)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \operatorname {BesselI}\left (0, \frac {2 x^{{3}/{2}} \sqrt {2}}{3}\right )+c_{2} \operatorname {BesselK}\left (0, \frac {2 x^{{3}/{2}} \sqrt {2}}{3}\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 65

DSolve[(4 - 2*x^3)*y[x] + 5*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 \sqrt [3]{3} c_2 K_0\left (\frac {2}{3} \sqrt {2} x^{3/2}\right )-3 \sqrt [3]{-3} c_1 \operatorname {BesselI}\left (0,\frac {2}{3} \sqrt {2} x^{3/2}\right )}{2^{2/3} x^2} \]