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 = 317.903 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 2.625 (sec), leaf count = 107
\[ \left \{ y \left ( x \right ) =0,[x \left ( {\it \_T} \right ) ={\frac {-12\,{{\it \_T}}^{5}+ \left ( -12\,a+15 \right ) {{\it \_T}}^{4}+ \left ( 16\,a-12\,b \right ) {{\it \_T}}^{3}+18\,b{{\it \_T}}^{2}+12\,{\it \_C1}\,c}{12\, \left ( {\it \_T}-1 \right ) ^{2}c}},y \left ( {\it \_T} \right ) ={\frac {-9\,{{\it \_T}}^{6}+ \left ( -8\,a+12 \right ) {{\it \_T}}^{5}+ \left ( 12\,a-6\,b \right ) {{\it \_T}}^{4}+12\,{{\it \_T}}^{3}b+12\,{\it \_C1}\,c{{\it \_T}}^{2}}{12\, \left ( {\it \_T}-1 \right ) ^{2}c}}] \right \} \] 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),'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]