Internal problem ID [8660]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1082.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 m -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {\left (m^{2}-v^{2}\right ) {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 85
dsolve(diff(diff(y(x),x),x)-(diff(diff(g(x),x),x)/diff(g(x),x)+(2*m-1)*diff(g(x),x)/g(x))*diff(y(x),x)+((m^2-v^2)*diff(g(x),x)^2/g(x)+diff(g(x),x)^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} g \left (x \right )^{2 m} {\mathrm e}^{-i g \left (x \right )} \operatorname {KummerM}\left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 1+2 m , 2 i g \left (x \right )\right )+c_{2} g \left (x \right )^{2 m} {\mathrm e}^{-i g \left (x \right )} \operatorname {KummerU}\left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 1+2 m , 2 i g \left (x \right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*(Derivative[1][g][x]^2 + ((m^2 - v^2)*Derivative[1][g][x]^2)/g[x]) - y'[x]*(((-1 + 2*m)*Derivative[1][g][x])/g[x] + Derivative[2][g][x]/Derivative[1][g][x]) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved