Internal problem ID [8612]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1032.
ODE order: 3.
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 \prime }\relax (x )}{2 g^{\prime }\relax (x )}-\frac {3 g^{\prime \prime }\relax (x )^{2}}{4 g^{\prime }\relax (x )^{2}}+\frac {\left (\frac {1}{4}-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: 53
dsolve(diff(diff(y(x),x),x)+(1/2*diff(diff(diff(g(x),x),x),x)/diff(g(x),x)-3/4*diff(diff(g(x),x),x)^2/diff(g(x),x)^2+(1/4-v^2)*diff(g(x),x)^2/g(x)+diff(g(x),x)^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \WhittakerM \left (\frac {1}{2} i v^{2}-\frac {1}{8} i, \frac {1}{2}, 2 i g \relax (x )\right )}{\sqrt {\frac {d}{d x}g \relax (x )}}+\frac {c_{2} \WhittakerW \left (\frac {1}{2} i v^{2}-\frac {1}{8} i, \frac {1}{2}, 2 i g \relax (x )\right )}{\sqrt {\frac {d}{d x}g \relax (x )}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*((g^3)[x]/(2*Derivative[1][g][x]) + Derivative[1][g][x]^2 + ((1/4 - v^2)*Derivative[1][g][x]^2)/g[x] - (3*Derivative[2][g][x]^2)/(4*Derivative[1][g][x]^2)) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved