4.17.41 \(4 y'(x)^2=9 x\)

ODE
\[ 4 y'(x)^2=9 x \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

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

\[\left \{\left \{y(x)\to c_1-x^{3/2}\right \},\left \{y(x)\to c_1+x^{3/2}\right \}\right \}\]

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

\[ \left \{ y \relax (x ) =-{x}^{{\frac {3}{2}}}+{\it \_C1},y \relax (x ) ={x}^{{\frac {3}{2}}}+{\it \_C1} \right \} \] 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