4.13.22 $(y(x)+x{)}^2{y}^{\prime }(x)=x^2-2xy(x)+5y(x{)}^2$

ODE
$$(y(x)+x{)}^2{y}^{\prime }(x)=x^2-2xy(x)+5y(x{)}^2$$ ODE Classification

[[_homogeneous, `class A`], _rational, _dAlembert]

Book solution method
Equation linear in the variables, $y^{\prime }(x)=f\left(\frac{X_1}{X_2}\right)$

Mathematica ✓
cpu = 0.252843 (sec), leaf count = 35

$$\text{Solve}[\frac{2x(x-2y(x))}{(x-y(x){)}^2}+\log (\frac{y(x)}{x}-1)+\log (x)=c_1,y(x)]$$

Maple ✓
cpu = 0.02 (sec), leaf count = 68

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

DSolve[(x + y[x])^2*y'[x] == x^2 - 2*x*y[x] + 5*y[x]^2,y[x],x]

Mathematica raw output

Solve[Log[x] + Log[-1 + y[x]/x] + (2*x*(x - 2*y[x]))/(x - y[x])^2 == C[1], y[x]]

Maple raw input

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

Maple raw output

((x-y(x))^2*ln((y(x)-x)/x)+(-_C1+ln(x))*y(x)^2+2*x*(_C1-ln(x)-2)*y(x)-x^2*(_C1-l
n(x)-2))/(x-y(x))^2 = 0