4.19.42 \(4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0\)

ODE
\[ 4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0 \] ODE Classification

[[_homogeneous, `class G`]]

Book solution method
No Missing Variables ODE, Solve for \(y\)

Mathematica
cpu = 0.706901 (sec), leaf count = 121

\[\left \{\text {Solve}\left [\log (x)=c_1+\frac {2 x^{5/2} \sqrt {1-x^3 y(x)^2} \sin ^{-1}\left (x^{3/2} y(x)\right )}{3 \sqrt {x^5 \left (x^3 y(x)^2-1\right )}},y(x)\right ],\text {Solve}\left [\frac {2 x^{5/2} \sqrt {1-x^3 y(x)^2} \sin ^{-1}\left (x^{3/2} y(x)\right )}{3 \sqrt {x^5 \left (x^3 y(x)^2-1\right )}}+\log (x)=c_1,y(x)\right ]\right \}\]

Maple
cpu = 0.158 (sec), leaf count = 67

\[ \left \{ \left (y \relax (x ) \right ) ^{2}-{x}^{-3}=0,{x}^{3}y \relax (x ) +x\sqrt {{x}^{4} \left (y \relax (x ) \right ) ^{2}-x}-{\it \_C1}=0,y \relax (x ) +{\frac {1}{{x}^{2}}\sqrt {{x}^{4} \left (y \relax (x ) \right ) ^{2}-x}}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[9 + 12*x^4*y[x]*y'[x] + 4*x^5*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{Solve[Log[x] == C[1] + (2*x^(5/2)*ArcSin[x^(3/2)*y[x]]*Sqrt[1 - x^3*y[x]^2])/(3
*Sqrt[x^5*(-1 + x^3*y[x]^2)]), y[x]], Solve[Log[x] + (2*x^(5/2)*ArcSin[x^(3/2)*y
[x]]*Sqrt[1 - x^3*y[x]^2])/(3*Sqrt[x^5*(-1 + x^3*y[x]^2)]) == C[1], y[x]]}

Maple raw input

dsolve(4*x^5*diff(y(x),x)^2+12*x^4*y(x)*diff(y(x),x)+9 = 0, y(x),'implicit')

Maple raw output

y(x)^2-1/x^3 = 0, y(x)+1/x^2*(x^4*y(x)^2-x)^(1/2)-_C1 = 0, x^3*y(x)+x*(x^4*y(x)^
2-x)^(1/2)-_C1 = 0