4.7.23 $(a+x{)}^2{y}^{\prime }(x)=2(a+x)(b+y(x))$

ODE
$$(a+x{)}^2{y}^{\prime }(x)=2(a+x)(b+y(x))$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.00965325 (sec), leaf count = 17

$$\left\{\{y(x)\to c_1(a+x{)}^2-b\}\right\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 15

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

DSolve[(a + x)^2*y'[x] == 2*(a + x)*(b + y[x]),y[x],x]

Mathematica raw output

{{y[x] -> -b + (a + x)^2*C[1]}}

Maple raw input

dsolve((a+x)^2*diff(y(x),x) = 2*(a+x)*(b+y(x)), y(x),'implicit')

Maple raw output

y(x) = -b+(a+x)^2*_C1