81.2.4 problem 4

Internal problem ID [18612]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 08:28:43 PM
CAS classification : [[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x$3)*diff(y(x),x)-3*diff(y(x),x$2)^2+3*diff(y(x),x$2)*diff(y(x),x)^2-2*diff(y(x),x)^4-x*diff(y(x),x)^5=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved