ODE
\[ y'(x)^4-3 (1-x) y'(x)^2+3 (1-2 y(x)) y'(x)+3 x=0 \] ODE Classification
odeadvisor timed out
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✓
cpu = 0.188144 (sec), leaf count = 77
\[\left \{\left \{y(x)\to \frac {1}{12} \left (-6 c_1 (x-1)-\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6-c_1{}^3\right )\right \},\left \{y(x)\to \frac {1}{12} \left (-6 c_1 (x-1)+\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6-c_1{}^3\right )\right \}\right \}\]
Maple ✓
cpu = 0.131 (sec), leaf count = 245
\[\left [y \left (x \right ) = -x +\frac {5}{6}, y \left (x \right ) = x +\frac {1}{6}, y \left (x \right ) = \frac {x \left (3 \left (-\frac {\textit {\_C1}}{2}-\frac {\sqrt {\textit {\_C1}^{2}+4 x}}{2}\right )^{2}+3\right )}{-3 \textit {\_C1} -3 \sqrt {\textit {\_C1}^{2}+4 x}}+\frac {\left (-\frac {\textit {\_C1}}{2}-\frac {\sqrt {\textit {\_C1}^{2}+4 x}}{2}\right )^{4}-3 \left (-\frac {\textit {\_C1}}{2}-\frac {\sqrt {\textit {\_C1}^{2}+4 x}}{2}\right )^{2}-\frac {3 \textit {\_C1}}{2}-\frac {3 \sqrt {\textit {\_C1}^{2}+4 x}}{2}}{-3 \textit {\_C1} -3 \sqrt {\textit {\_C1}^{2}+4 x}}, y \left (x \right ) = \frac {\left (3 \left (-\frac {\textit {\_C1}}{2}+\frac {\sqrt {\textit {\_C1}^{2}+4 x}}{2}\right )^{2}+3\right ) x}{-3 \textit {\_C1} +3 \sqrt {\textit {\_C1}^{2}+4 x}}+\frac {\left (-\frac {\textit {\_C1}}{2}+\frac {\sqrt {\textit {\_C1}^{2}+4 x}}{2}\right )^{4}-3 \left (-\frac {\textit {\_C1}}{2}+\frac {\sqrt {\textit {\_C1}^{2}+4 x}}{2}\right )^{2}-\frac {3 \textit {\_C1}}{2}+\frac {3 \sqrt {\textit {\_C1}^{2}+4 x}}{2}}{-3 \textit {\_C1} +3 \sqrt {\textit {\_C1}^{2}+4 x}}\right ]\] Mathematica raw input
DSolve[3*x + 3*(1 - 2*y[x])*y'[x] - 3*(1 - x)*y'[x]^2 + y'[x]^4 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (6 - 6*(-1 + x)*C[1] - C[1]^3 - Sqrt[(4*x + C[1]^2)^3])/12}, {y[x] -> (6 - 6*(-1 + x)*C[1] - C[1]^3 + Sqrt[(4*x + C[1]^2)^3])/12}}
Maple raw input
dsolve(diff(y(x),x)^4-3*(1-x)*diff(y(x),x)^2+3*(1-2*y(x))*diff(y(x),x)+3*x = 0, y(x))
Maple raw output
[y(x) = -x+5/6, y(x) = x+1/6, y(x) = 1/6*(3*(-1/2*_C1-1/2*(_C1^2+4*x)^(1/2))^2+3)/(-1/2*_C1-1/2*(_C1^2+4*x)^(1/2))*x+1/6*((-1/2*_C1-1/2*(_C1^2+4*x)^(1/2))^4-3*(-1/2*_C1-1/2*(_C1^2+4*x)^(1/2))^2-3/2*_C1-3/2*(_C1^2+4*x)^(1/2))/(-1/2*_C1-1/2*(_C1^2+4*x)^(1/2)), y(x) = 1/6*(3*(-1/2*_C1+1/2*(_C1^2+4*x)^(1/2))^2+3)/(-1/2*_C1+1/2*(_C1^2+4*x)^(1/2))*x+1/6*((-1/2*_C1+1/2*(_C1^2+4*x)^(1/2))^4-3*(-1/2*_C1+1/2*(_C1^2+4*x)^(1/2))^2-3/2*_C1+3/2*(_C1^2+4*x)^(1/2))/(-1/2*_C1+1/2*(_C1^2+4*x)^(1/2))]