ODE
\[ -a-3 y(x)^5 y'(x)+9 x y(x)^4 y'(x)^2=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.493587 (sec), leaf count = 307
\[\left \{\left \{y(x)\to -\frac {i \left (\cosh \left (\frac {c_1}{6}\right )-\sinh \left (\frac {c_1}{6}\right )\right ) \sqrt [3]{4 a x+\sinh \left (c_1\right )+\cosh \left (c_1\right )}}{\sqrt [3]{2}}\right \},\left \{y(x)\to \frac {i \left (\cosh \left (\frac {c_1}{6}\right )-\sinh \left (\frac {c_1}{6}\right )\right ) \sqrt [3]{4 a x+\sinh \left (c_1\right )+\cosh \left (c_1\right )}}{\sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (\sqrt {3}-i\right ) \left (\cosh \left (\frac {c_1}{6}\right )-\sinh \left (\frac {c_1}{6}\right )\right ) \sqrt [3]{4 a x+\sinh \left (c_1\right )+\cosh \left (c_1\right )}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\left (\sqrt {3}-i\right ) \left (\cosh \left (\frac {c_1}{6}\right )-\sinh \left (\frac {c_1}{6}\right )\right ) \sqrt [3]{4 a x+\sinh \left (c_1\right )+\cosh \left (c_1\right )}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\left (\sqrt {3}+i\right ) \left (\cosh \left (\frac {c_1}{6}\right )-\sinh \left (\frac {c_1}{6}\right )\right ) \sqrt [3]{4 a x+\sinh \left (c_1\right )+\cosh \left (c_1\right )}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (\sqrt {3}+i\right ) \left (\cosh \left (\frac {c_1}{6}\right )-\sinh \left (\frac {c_1}{6}\right )\right ) \sqrt [3]{4 a x+\sinh \left (c_1\right )+\cosh \left (c_1\right )}}{2 \sqrt [3]{2}}\right \}\right \}\]
Maple ✓
cpu = 0.162 (sec), leaf count = 104
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{6}+4\,ax=0,-\ln \left ( x \right ) -\ln \left ( - \left ( y \left ( x \right ) \right ) ^{3}+\sqrt { \left ( y \left ( x \right ) \right ) ^{6}+4\,ax} \right ) +\ln \left ( \left ( y \left ( x \right ) \right ) ^{3}+\sqrt { \left ( y \left ( x \right ) \right ) ^{6}+4\,ax} \right ) +{\it \_C1}=0,-\ln \left ( x \right ) +\ln \left ( - \left ( y \left ( x \right ) \right ) ^{3}+\sqrt { \left ( y \left ( x \right ) \right ) ^{6}+4\,ax} \right ) -\ln \left ( \left ( y \left ( x \right ) \right ) ^{3}+\sqrt { \left ( y \left ( x \right ) \right ) ^{6}+4\,ax} \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[-a - 3*y[x]^5*y'[x] + 9*x*y[x]^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*(Cosh[C[1]/6] - Sinh[C[1]/6])*(4*a*x + Cosh[C[1]] + Sinh[C[1]])^(1/3))/2^(1/3)}, {y[x] -> (I*(Cosh[C[1]/6] - Sinh[C[1]/6])*(4*a*x + Cosh[C[1]] + Sinh[C[1]])^(1/3))/2^(1/3)}, {y[x] -> ((-I + Sqrt[3])*(Cosh[C[1]/6] - Sinh[C[1]/6])*(4*a*x + Cosh[C[1]] + Sinh[C[1]])^(1/3))/(2*2^(1/3))}, {y[x] -> -((-I + Sqrt[3])*(Cosh[C[1]/6] - Sinh[C[1]/6])*(4*a*x + Cosh[C[1]] + Sinh[C[1]])^(1/3))/(2*2^(1/3))}, {y[x] -> -((I + Sqrt[3])*(Cosh[C[1]/6] - Sinh[C[1]/6])*(4*a*x + Cosh[C[1]] + Sinh[C[1]])^(1/3))/(2*2^(1/3))}, {y[x] -> ((I + Sqrt[3])*(Cosh[C[1]/6] - Sinh[C[1]/6])*(4*a*x + Cosh[C[1]] + Sinh[C[1]])^(1/3))/(2*2^(1/3))}}
Maple raw input
dsolve(9*x*y(x)^4*diff(y(x),x)^2-3*y(x)^5*diff(y(x),x)-a = 0, y(x),'implicit')
Maple raw output
y(x)^6+4*a*x = 0, -ln(x)+ln(-y(x)^3+(y(x)^6+4*a*x)^(1/2))-ln(y(x)^3+(y(x)^6+4*a*x)^(1/2))+_C1 = 0, -ln(x)-ln(-y(x)^3+(y(x)^6+4*a*x)^(1/2))+ln(y(x)^3+(y(x)^6+4*a*x)^(1/2))+_C1 = 0