60.8.15 problem 1851

Internal problem ID [11850]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1851
Date solved : Monday, January 27, 2025 at 11:43:47 PM
CAS classification : [NONE]

\begin{align*} y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+{y^{\prime }}^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right ) y^{\prime \prime }\right )+2 q \left (x \right ) {y^{\prime }}^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right )&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[2*q[x]*Sin[y[x]]*D[y[x],x]^2 + D[y[x],x]^3*(Derivative[1][f][x]*D[y[x],x] + f[x]*D[y[x],{x,2}]) + Cos[y[x]]*(-(Derivative[1][q][x]*D[y[x],x]) + q[x]*D[y[x],{x,2}]) - D[y[x],{x,2}]*(D[y[x],x]*Derivative[2][f][x] + 2*Derivative[1][f][x]*D[y[x],{x,2}] + f[x]*Derivative[3][y][x]) + D[y[x],x]*(3*Derivative[2][f][x]*D[y[x],{x,2}] + D[y[x],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