4.17.41 $4y^{\prime }(x{)}^2=9x$

ODE
$$4y^{\prime }(x{)}^2=9x$$ ODE Classification

[_quadrature]

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

Mathematica ✓
cpu = 0.00518793 (sec), leaf count = 27

$$\{\{y(x)\to c_1-x^{3/2}\},\{y(x)\to c_1+x^{3/2}\}\}$$

Maple ✓
cpu = 0.023 (sec), leaf count = 19

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

DSolve[4*y'[x]^2 == 9*x,y[x],x]

Mathematica raw output

{{y[x] -> -x^(3/2) + C[1]}, {y[x] -> x^(3/2) + C[1]}}

Maple raw input

dsolve(4*diff(y(x),x)^2 = 9*x, y(x),'implicit')

Maple raw output

y(x) = -x^(3/2)+_C1, y(x) = x^(3/2)+_C1