ODE
\[ x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.66764 (sec), leaf count = 259
\[\left \{\left \{y(x)\to -i x \log \left (-\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}+i \sinh \left (c_2\right )+i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {-\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}+i \sinh \left (c_2\right )+i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}-i \sinh \left (c_2\right )-i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}+i \sinh \left (c_2\right )+i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.151 (sec), leaf count = 47
\[ \left \{ {\frac {y \left ( x \right ) }{x}}-\arctan \left ( {\frac {1}{\sqrt {{\it \_C1}\,{x}^{2}-1}}} \right ) -{\it \_C2}=0,{\frac {y \left ( x \right ) }{x}}+\arctan \left ( {\frac {1}{\sqrt {{\it \_C1}\,{x}^{2}-1}}} \right ) -{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[(-y[x] + x*y'[x])^3 + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-I)*x*Log[-(I*Cosh[C[2]] + I*Sinh[C[2]] + Sqrt[(-8*I)*x^2*C[1] - Cosh[2*C[2]] - Sinh[2*C[2]]])/(4*x*C[1])]}, {y[x] -> (-I)*x*Log[(I*Cosh[C[2]] + I*Sinh[C[2]] - Sqrt[(-8*I)*x^2*C[1] - Cosh[2*C[2]] - Sinh[2*C[2]]])/(4*x*C[1])]}, {y[x] -> (-I)*x*Log[((-I)*Cosh[C[2]] - I*Sinh[C[2]] + Sqrt[(-8*I)*x^2*C[1] - Cosh[2*C[2]] - Sinh[2*C[2]]])/(4*x*C[1])]}, {y[x] -> (-I)*x*Log[(I*Cosh[C[2]] + I*Sinh[C[2]] + Sqrt[(-8*I)*x^2*C[1] - Cosh[2*C[2]] - Sinh[2*C[2]]])/(4*x*C[1])]}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^3 = 0, y(x),'implicit')
Maple raw output
y(x)/x+arctan(1/(_C1*x^2-1)^(1/2))-_C2 = 0, y(x)/x-arctan(1/(_C1*x^2-1)^(1/2))-_C2 = 0