ODE
\[ 4 y'(x)^3+4 y'(x)=x \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)
Mathematica ✓
cpu = 0.935088 (sec), leaf count = 390
\[\left \{\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (-27 x^2+3 \sqrt {81 x^2+192} x+32\right )}{16\ 3^{2/3} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}+\frac {\left (1+i \sqrt {3}\right ) \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}{12 \sqrt [3]{3}}+\frac {-8-8 i \sqrt {3}}{\sqrt [3]{3} \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+c_1\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (-27 x^2+3 \sqrt {81 x^2+192} x+32\right )}{16\ 3^{2/3} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}+\frac {\left (1-i \sqrt {3}\right ) \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}{12 \sqrt [3]{3}}+\frac {8 i \left (\sqrt {3}+i\right )}{\sqrt [3]{3} \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+c_1\right \},\left \{y(x)\to \frac {\left (\sqrt {81 x^2+192}-9 x\right )^{8/3}-384 \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}+8 \sqrt [3]{3} \left (96-\left (\sqrt {81 x^2+192}-9 x\right )^2\right )}{48\ 3^{2/3} \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.33 (sec), leaf count = 199
\[\left [y \left (x \right ) = \int \frac {i \left (\sqrt {3}\, \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}+12 \sqrt {3}+i \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}-12 i\right )}{12 \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {1}{3}}}d x +\textit {\_C1}, y \left (x \right ) = \int \frac {i \left (i \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}-\sqrt {3}\, \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}-12 i-12 \sqrt {3}\right )}{12 \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {1}{3}}}d x +\textit {\_C1}, y \left (x \right ) = \int \frac {\left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}-12}{6 \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {1}{3}}}d x +\textit {\_C1}\right ]\] Mathematica raw input
DSolve[4*y'[x] + 4*y'[x]^3 == x,y[x],x]
Mathematica raw output
{{y[x] -> (-8 - (8*I)*Sqrt[3])/(3^(1/3)*(-9*x + Sqrt[192 + 81*x^2])^(4/3)) + ((1 + I*Sqrt[3])*(-9*x + Sqrt[192 + 81*x^2])^(2/3))/(12*3^(1/3)) + ((1 - I*Sqrt[3])*(32 - 27*x^2 + 3*x*Sqrt[192 + 81*x^2]))/(16*3^(2/3)*(-9*x + Sqrt[192 + 81*x^2])^(2/3)) + C[1]}, {y[x] -> ((8*I)*(I + Sqrt[3]))/(3^(1/3)*(-9*x + Sqrt[192 + 81*x^2])^(4/3)) + ((1 - I*Sqrt[3])*(-9*x + Sqrt[192 + 81*x^2])^(2/3))/(12*3^(1/3)) + ((1 + I*Sqrt[3])*(32 - 27*x^2 + 3*x*Sqrt[192 + 81*x^2]))/(16*3^(2/3)*(-9*x + Sqrt[192 + 81*x^2])^(2/3)) + C[1]}, {y[x] -> (-384*(-9*x + Sqrt[192 + 81*x^2])^(2/3) + (-9*x + Sqrt[192 + 81*x^2])^(8/3) + 8*3^(1/3)*(96 - (-9*x + Sqrt[192 + 81*x^2])^2))/(48*3^(2/3)*(-9*x + Sqrt[192 + 81*x^2])^(4/3)) + C[1]}}
Maple raw input
dsolve(4*diff(y(x),x)^3+4*diff(y(x),x) = x, y(x))
Maple raw output
[y(x) = Int(1/12*I*(3^(1/2)*(27*x+3*(81*x^2+192)^(1/2))^(2/3)+12*3^(1/2)+I*(27*x+3*(81*x^2+192)^(1/2))^(2/3)-12*I)/(27*x+3*(81*x^2+192)^(1/2))^(1/3),x)+_C1, y(x) = Int(1/12*I*(I*(27*x+3*(81*x^2+192)^(1/2))^(2/3)-3^(1/2)*(27*x+3*(81*x^2+192)^(1/2))^(2/3)-12*I-12*3^(1/2))/(27*x+3*(81*x^2+192)^(1/2))^(1/3),x)+_C1, y(x) = Int(1/6*((27*x+3*(81*x^2+192)^(1/2))^(2/3)-12)/(27*x+3*(81*x^2+192)^(1/2))^(1/3),x)+_C1]