Internal problem ID [9023]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1444.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {a f^{\prime }\relax (x ) y^{\prime }}{f \relax (x )}+\frac {b f \relax (x )^{2 a +1} y}{f \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(diff(y(x),x),x) = a*diff(f(x),x)/f(x)*diff(y(x),x)-b*f(x)^(2*a+1)/f(x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\int i f \relax (x )^{a} \sqrt {b}d x}+c_{2} {\mathrm e}^{-\left (\int i f \relax (x )^{a} \sqrt {b}d x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -(b*f[x]^(2*a)*y[x]) - (a*Derivative[1][f][x]*y'[x])/f[x],y[x],x,IncludeSingularSolutions -> True]
Not solved