ODE
\[ a y'(x)^4+b y'(x)^3+c x y'(x)^2+y'(x)^5=c y(x) \] ODE Classification
[_dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✓
cpu = 15.7847 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 1.747 (sec), leaf count = 126
\[\left [y \left (x \right ) = 0, \left [x \left (\textit {\_T} \right ) = \frac {\frac {-\textit {\_T}^{5}+\frac {\left (5-4 a \right ) \textit {\_T}^{4}}{4}+\frac {\left (4 a -3 b \right ) \textit {\_T}^{3}}{3}+\frac {3 b \,\textit {\_T}^{2}}{2}}{c}+\textit {\_C1}}{\left (\textit {\_T} -1\right )^{2}}, y \left (\textit {\_T} \right ) = \frac {\left (\frac {-\textit {\_T}^{5}+\frac {\left (5-4 a \right ) \textit {\_T}^{4}}{4}+\frac {\left (4 a -3 b \right ) \textit {\_T}^{3}}{3}+\frac {3 b \,\textit {\_T}^{2}}{2}}{c}+\textit {\_C1} \right ) \textit {\_T}^{2}}{\left (\textit {\_T} -1\right )^{2}}+\frac {\textit {\_T}^{5}+\textit {\_T}^{4} a +\textit {\_T}^{3} b}{c}\right ]\right ]\] Mathematica raw input
DSolve[c*x*y'[x]^2 + b*y'[x]^3 + a*y'[x]^4 + y'[x]^5 == c*y[x],y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^5+a*diff(y(x),x)^4+b*diff(y(x),x)^3+c*x*diff(y(x),x)^2 = c*y(x), y(x))
Maple raw output
[y(x) = 0, [x(_T) = 1/(_T-1)^2*(1/c*(-_T^5+1/4*(5-4*a)*_T^4+1/3*(4*a-3*b)*_T^3+3/2*b*_T^2)+_C1), y(_T) = 1/(_T-1)^2*(1/c*(-_T^5+1/4*(5-4*a)*_T^4+1/3*(4*a-3*b)*_T^3+3/2*b*_T^2)+_C1)*_T^2+(_T^5+_T^4*a+_T^3*b)/c]]