60.8.16 problem 1852

Internal problem ID [11851]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1852
Date solved : Monday, January 27, 2025 at 11:43:47 PM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.113 (sec). Leaf size: 36

dsolve(3*diff(diff(y(x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= c_{1} x +c_{2} \\ y &= 3 \left (x +c_{2} \right ) \sqrt {6}\, c_{1} \sqrt {-\frac {c_{1}}{x +c_{2}}}+x c_3 +c_4 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 28

DSolve[-5*Derivative[3][y][x]^2 + 3*D[y[x],{x,2}]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \left (-\sqrt {2 x+3 c_1}\right )+c_4 x+c_3 \]