4.15.20 $y(x{)}^3(3x^{5}y(x{)}^5-1)+x^3(5x^{3}y(x{)}^7+1)y^{\prime }(x)=0$

ODE
$$y(x{)}^3(3x^{5}y(x{)}^5-1)+x^3(5x^{3}y(x{)}^7+1)y^{\prime }(x)=0$$ ODE Classification

[_rational]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0246112 (sec), leaf count = 253

$$\{\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},1]\},\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},2]\},\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},3]\},\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},4]\},\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},5]\},\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},6]\},\{y(x)\to \text{Root}[2{\mathrm{\#}\text{1}}^7{x}^5+{\mathrm{\#}\text{1}}^2(1-2c_1{x}^2)-x^2\mathrm{\&},7]\}\}$$

Maple ✓
cpu = 0.172 (sec), leaf count = 25

$$\{-x^3{\left(y\left(x\right)\right)}^5-\frac{1}{2x^2}+\frac{1}{2{\left(y\left(x\right)\right)}^2}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[y[x]^3*(-1 + 3*x^5*y[x]^5) + x^3*(1 + 5*x^3*y[x]^7)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> Root[-x^2 + (1 - 2*x^2*C[1])*#1^2 + 2*x^5*#1^7 & , 1]}, {y[x] -> Root[
-x^2 + (1 - 2*x^2*C[1])*#1^2 + 2*x^5*#1^7 & , 2]}, {y[x] -> Root[-x^2 + (1 - 2*x
^2*C[1])*#1^2 + 2*x^5*#1^7 & , 3]}, {y[x] -> Root[-x^2 + (1 - 2*x^2*C[1])*#1^2 +
 2*x^5*#1^7 & , 4]}, {y[x] -> Root[-x^2 + (1 - 2*x^2*C[1])*#1^2 + 2*x^5*#1^7 & ,
 5]}, {y[x] -> Root[-x^2 + (1 - 2*x^2*C[1])*#1^2 + 2*x^5*#1^7 & , 6]}, {y[x] -> 
Root[-x^2 + (1 - 2*x^2*C[1])*#1^2 + 2*x^5*#1^7 & , 7]}}

Maple raw input

dsolve(x^3*(1+5*x^3*y(x)^7)*diff(y(x),x)+(3*x^5*y(x)^5-1)*y(x)^3 = 0, y(x),'implicit')

Maple raw output

-x^3*y(x)^5-1/2/x^2+1/2/y(x)^2+_C1 = 0