4.23.3 $a{y}^{\prime }(x{)}^4+b{y}^{\prime }(x{)}^3+cx{y}^{\prime }(x{)}^2+y^{\prime }(x{)}^5=cy(x)$

ODE
$$a{y}^{\prime }(x{)}^4+b{y}^{\prime }(x{)}^3+cx{y}^{\prime }(x{)}^2+y^{\prime }(x{)}^5=cy(x)$$ ODE Classification

[_dAlembert]

Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Mathematica ✓
cpu = 317.903 (sec), leaf count = 1

$$\mathrm{\$}\text{Aborted}$$

Maple ✓
cpu = 2.625 (sec), leaf count = 107

$$\{y\left(x\right)=0,[x\left(\mathit{\_}\mathit{T}\right)=\frac{-12{\mathit{\_}\mathit{T}}^5+(-12a+15){\mathit{\_}\mathit{T}}^4+(16a-12b){\mathit{\_}\mathit{T}}^3+18b{\mathit{\_}\mathit{T}}^2+12\mathit{\_}\mathit{C}\mathit{1}c}{12{(\mathit{\_}\mathit{T}-1)}^{2}c},y\left(\mathit{\_}\mathit{T}\right)=\frac{-9{\mathit{\_}\mathit{T}}^6+(-8a+12){\mathit{\_}\mathit{T}}^5+(12a-6b){\mathit{\_}\mathit{T}}^4+12{\mathit{\_}\mathit{T}}^{3}b+12\mathit{\_}\mathit{C}\mathit{1}c{\mathit{\_}\mathit{T}}^2}{12{(\mathit{\_}\mathit{T}-1)}^{2}c}]\}$$ 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),'implicit')

Maple raw output

y(x) = 0, [x(_T) = 1/12*(-12*_T^5+(-12*a+15)*_T^4+(16*a-12*b)*_T^3+18*b*_T^2+12*
_C1*c)/(_T-1)^2/c, y(_T) = 1/12*(-9*_T^6+(-8*a+12)*_T^5+(12*a-6*b)*_T^4+12*_T^3*
b+12*_C1*c*_T^2)/(_T-1)^2/c]