Internal problem ID [8662]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (\frac {g^{\prime \prime }\relax (x )}{g^{\prime }\relax (x )}+\frac {\left (2 m -1\right ) g^{\prime }\relax (x )}{g \relax (x )}\right ) y^{\prime }+\left (\frac {\left (m^{2}-v^{2}\right ) g^{\prime }\relax (x )^{2}}{g \relax (x )}+g^{\prime }\relax (x )^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-i g \relax (x )} \KummerM \left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 1+2 m , 2 i g \relax (x )\right ) g \relax (x )^{2 m}+c_{2} {\mathrm e}^{-i g \relax (x )} \KummerU \left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 1+2 m , 2 i g \relax (x )\right ) g \relax (x )^{2 m} \]
✗ 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