4.844   5y′(x)2 + 3xy′(x)− y(x) = 0

ODE

5y′(x)2 + 3xy′(x)− y(x) = 0

ODE Classification

[[_1st_order, _with_linear_symmetries], _dAlembert]

Book solution method
No Missing Variables ODE, Solve for y

Mathematica
cpu = 0.297902 (sec), leaf count = 771

{{y(x) → Root[80#15 + 40#14x2 + 5#13x4 − 4000#12e5c1x− 1800#1e5c1x3 − 216e5c1x5 − 40000e10c1&,1]} ,{y (x) → Root [80#15 + 40#14x2 + 5#13x4 − 4000#12e5c1x− 1800#1e5c1x3 − 216e5c1x5 − 40000e10c1

Maple
cpu = 0.018 (sec), leaf count = 32

{          (    5∕2     )   − 3        (    5       )  1  }
 [x(-T) = 1 − 2-T  + -C1  T  2,y(-T) = 1 −-T2 + 3 C1 √--T]

Mathematica raw input

DSolve[-y[x] + 3*x*y'[x] + 5*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> Root[-40000*E^(10*C[1]) - 216*E^(5*C[1])*x^5 - 1800*E^(5*C[1])*x^3*#1 
- 4000*E^(5*C[1])*x*#1^2 + 5*x^4*#1^3 + 40*x^2*#1^4 + 80*#1^5 & , 1]}, {y[x] -> 
Root[-40000*E^(10*C[1]) - 216*E^(5*C[1])*x^5 - 1800*E^(5*C[1])*x^3*#1 - 4000*E^(
5*C[1])*x*#1^2 + 5*x^4*#1^3 + 40*x^2*#1^4 + 80*#1^5 & , 2]}, {y[x] -> Root[-4000
0*E^(10*C[1]) - 216*E^(5*C[1])*x^5 - 1800*E^(5*C[1])*x^3*#1 - 4000*E^(5*C[1])*x*
#1^2 + 5*x^4*#1^3 + 40*x^2*#1^4 + 80*#1^5 & , 3]}, {y[x] -> Root[-40000*E^(10*C[
1]) - 216*E^(5*C[1])*x^5 - 1800*E^(5*C[1])*x^3*#1 - 4000*E^(5*C[1])*x*#1^2 + 5*x
^4*#1^3 + 40*x^2*#1^4 + 80*#1^5 & , 4]}, {y[x] -> Root[-40000*E^(10*C[1]) - 216*
E^(5*C[1])*x^5 - 1800*E^(5*C[1])*x^3*#1 - 4000*E^(5*C[1])*x*#1^2 + 5*x^4*#1^3 + 
40*x^2*#1^4 + 80*#1^5 & , 5]}, {y[x] -> Root[-5*E^(10*C[1]) + 216*E^(5*C[1])*x^5
 + 1800*E^(5*C[1])*x^3*#1 + 4000*E^(5*C[1])*x*#1^2 + 40000*x^4*#1^3 + 320000*x^2
*#1^4 + 640000*#1^5 & , 1]}, {y[x] -> Root[-5*E^(10*C[1]) + 216*E^(5*C[1])*x^5 +
 1800*E^(5*C[1])*x^3*#1 + 4000*E^(5*C[1])*x*#1^2 + 40000*x^4*#1^3 + 320000*x^2*#
1^4 + 640000*#1^5 & , 2]}, {y[x] -> Root[-5*E^(10*C[1]) + 216*E^(5*C[1])*x^5 + 1
800*E^(5*C[1])*x^3*#1 + 4000*E^(5*C[1])*x*#1^2 + 40000*x^4*#1^3 + 320000*x^2*#1^
4 + 640000*#1^5 & , 3]}, {y[x] -> Root[-5*E^(10*C[1]) + 216*E^(5*C[1])*x^5 + 180
0*E^(5*C[1])*x^3*#1 + 4000*E^(5*C[1])*x*#1^2 + 40000*x^4*#1^3 + 320000*x^2*#1^4 
+ 640000*#1^5 & , 4]}, {y[x] -> Root[-5*E^(10*C[1]) + 216*E^(5*C[1])*x^5 + 1800*
E^(5*C[1])*x^3*#1 + 4000*E^(5*C[1])*x*#1^2 + 40000*x^4*#1^3 + 320000*x^2*#1^4 + 
640000*#1^5 & , 5]}}

Maple raw input

dsolve(5*diff(y(x),x)^2+3*x*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

[x(_T) = 1/_T^(3/2)*(-2*_T^(5/2)+_C1), y(_T) = (-_T^(5/2)+3*_C1)/_T^(1/2)]