4.18.45 $x^2{y}^{\prime }(x{)}^2=a^2$

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

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.00319314 (sec), leaf count = 24

$$\{\{y(x)\to c_1-a\log (x)\},\{y(x)\to a\log (x)+c_1\}\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 20

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

DSolve[x^2*y'[x]^2 == a^2,y[x],x]

Mathematica raw output

{{y[x] -> C[1] - a*Log[x]}, {y[x] -> C[1] + a*Log[x]}}

Maple raw input

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

Maple raw output

y(x) = a*ln(x)+_C1, y(x) = -a*ln(x)+_C1