Internal problem ID [9430]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1851.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime } \left (f^{\prime \prime \prime }\relax (x ) y^{\prime }+3 f^{\prime \prime }\relax (x ) y^{\prime \prime }+3 f^{\prime }\relax (x ) y^{\prime \prime \prime }+f \relax (x ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+\left (y^{\prime }\right )^{3} \left (f^{\prime }\relax (x ) y^{\prime }+y^{\prime \prime } f \relax (x )\right )+2 q \relax (x ) \left (y^{\prime }\right )^{2} \sin \relax (y)+\left (q \relax (x ) y^{\prime \prime }-q^{\prime }\relax (x ) y^{\prime }\right ) \cos \relax (y)=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)*(diff(diff(diff(f(x),x),x),x)*diff(y(x),x)+3*diff(diff(f(x),x),x)*diff(diff(y(x),x),x)+3*diff(f(x),x)*diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(diff(diff(y(x),x),x),x),x))-diff(diff(y(x),x),x)*f*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^3*(diff(f(x),x)*diff(y(x),x)+f(x)*diff(diff(y(x),x),x))+2*q(x)*diff(y(x),x)^2*sin(y(x))+(q(x)*diff(diff(y(x),x),x)-diff(q(x),x)*diff(y(x),x))*cos(y(x))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*q[x]*Sin[y[x]]*y'[x]^2 + y'[x]^3*(Derivative[1][f][x]*y'[x] + f[x]*y''[x]) + Cos[y[x]]*(-(Derivative[1][q][x]*y'[x]) + q[x]*y''[x]) - y''[x]*(y'[x]*Derivative[2][f][x] + 2*Derivative[1][f][x]*y''[x] + f[x]*Derivative[3][y][x]) + y'[x]*(3*Derivative[2][f][x]*y''[x] + y'[x]*Derivative[3][f][x] + 3*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x]) == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved