ODE
\[ a-b x+y'(x)^3+y'(x)=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)
Mathematica ✓
cpu = 1.10625 (sec), leaf count = 677
\[\left \{\left \{y(x)\to \frac {\left (\sqrt {3} \sqrt {27 a^2-54 a b x+27 b^2 x^2+4}-9 a+9 b x\right )^2-24}{24 \sqrt [3]{2} 3^{2/3} b \left (\sqrt {3} \sqrt {27 a^2-54 a b x+27 b^2 x^2+4}-9 a+9 b x\right )^{2/3}}-\frac {\left (\sqrt {729 a^2-1458 a b x+729 b^2 x^2+108}-27 a+27 b x\right )^{2/3}}{18\ 2^{2/3} b}+\frac {3}{2^{2/3} b \left (\sqrt {729 a^2-1458 a b x+729 b^2 x^2+108}-27 a+27 b x\right )^{4/3}}+c_1\right \},\left \{y(x)\to \frac {\left (-1+i \sqrt {3}\right ) \left (\left (\sqrt {3} \sqrt {27 a^2-54 a b x+27 b^2 x^2+4}-9 a+9 b x\right )^2-24\right )}{48 \sqrt [3]{2} 3^{2/3} b \left (\sqrt {3} \sqrt {27 a^2-54 a b x+27 b^2 x^2+4}-9 a+9 b x\right )^{2/3}}+\frac {\left (1+i \sqrt {3}\right ) \left (\sqrt {729 a^2-1458 a b x+729 b^2 x^2+108}-27 a+27 b x\right )^{2/3}}{36\ 2^{2/3} b}-\frac {3 \left (1+i \sqrt {3}\right )}{2\ 2^{2/3} b \left (\sqrt {729 a^2-1458 a b x+729 b^2 x^2+108}-27 a+27 b x\right )^{4/3}}+c_1\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \left (\left (\sqrt {3} \sqrt {27 a^2-54 a b x+27 b^2 x^2+4}-9 a+9 b x\right )^2-24\right )}{48 \sqrt [3]{2} 3^{2/3} b \left (\sqrt {3} \sqrt {27 a^2-54 a b x+27 b^2 x^2+4}-9 a+9 b x\right )^{2/3}}+\frac {\left (1-i \sqrt {3}\right ) \left (\sqrt {729 a^2-1458 a b x+729 b^2 x^2+108}-27 a+27 b x\right )^{2/3}}{36\ 2^{2/3} b}-\frac {3 \left (1-i \sqrt {3}\right )}{2\ 2^{2/3} b \left (\sqrt {729 a^2-1458 a b x+729 b^2 x^2+108}-27 a+27 b x\right )^{4/3}}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.309 (sec), leaf count = 335
\[\left [y \left (x \right ) = \int \frac {i \left (\sqrt {3}\, \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {2}{3}}+12 \sqrt {3}+i \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {2}{3}}-12 i\right )}{12 \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +\textit {\_C1}, y \left (x \right ) = \int \frac {i \left (i \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {2}{3}}-\sqrt {3}\, \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {2}{3}}-12 i-12 \sqrt {3}\right )}{12 \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +\textit {\_C1}, y \left (x \right ) = \int \frac {\left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {2}{3}}-12}{6 \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 a b x +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +\textit {\_C1}\right ]\] Mathematica raw input
DSolve[a - b*x + y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> 3/(2^(2/3)*b*(-27*a + 27*b*x + Sqrt[108 + 729*a^2 - 1458*a*b*x + 729*b^2*x^2])^(4/3)) - (-27*a + 27*b*x + Sqrt[108 + 729*a^2 - 1458*a*b*x + 729*b^2*x^2])^(2/3)/(18*2^(2/3)*b) + (-24 + (-9*a + 9*b*x + Sqrt[3]*Sqrt[4 + 27*a^2 - 54*a*b*x + 27*b^2*x^2])^2)/(24*2^(1/3)*3^(2/3)*b*(-9*a + 9*b*x + Sqrt[3]*Sqrt[4 + 27*a^2 - 54*a*b*x + 27*b^2*x^2])^(2/3)) + C[1]}, {y[x] -> (-3*(1 + I*Sqrt[3]))/(2*2^(2/3)*b*(-27*a + 27*b*x + Sqrt[108 + 729*a^2 - 1458*a*b*x + 729*b^2*x^2])^(4/3)) + ((1 + I*Sqrt[3])*(-27*a + 27*b*x + Sqrt[108 + 729*a^2 - 1458*a*b*x + 729*b^2*x^2])^(2/3))/(36*2^(2/3)*b) + ((-1 + I*Sqrt[3])*(-24 + (-9*a + 9*b*x + Sqrt[3]*Sqrt[4 + 27*a^2 - 54*a*b*x + 27*b^2*x^2])^2))/(48*2^(1/3)*3^(2/3)*b*(-9*a + 9*b*x + Sqrt[3]*Sqrt[4 + 27*a^2 - 54*a*b*x + 27*b^2*x^2])^(2/3)) + C[1]}, {y[x] -> (-3*(1 - I*Sqrt[3]))/(2*2^(2/3)*b*(-27*a + 27*b*x + Sqrt[108 + 729*a^2 - 1458*a*b*x + 729*b^2*x^2])^(4/3)) + ((1 - I*Sqrt[3])*(-27*a + 27*b*x + Sqrt[108 + 729*a^2 - 1458*a*b*x + 729*b^2*x^2])^(2/3))/(36*2^(2/3)*b) - ((1 + I*Sqrt[3])*(-24 + (-9*a + 9*b*x + Sqrt[3]*Sqrt[4 + 27*a^2 - 54*a*b*x + 27*b^2*x^2])^2))/(48*2^(1/3)*3^(2/3)*b*(-9*a + 9*b*x + Sqrt[3]*Sqrt[4 + 27*a^2 - 54*a*b*x + 27*b^2*x^2])^(2/3)) + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^3+diff(y(x),x)+a-b*x = 0, y(x))
Maple raw output
[y(x) = Int(1/12*I*(3^(1/2)*(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(2/3)+12*3^(1/2)+I*(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(2/3)-12*I)/(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(1/3),x)+_C1, y(x) = Int(1/12*I*(I*(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(2/3)-3^(1/2)*(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(2/3)-12*I-12*3^(1/2))/(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(1/3),x)+_C1, y(x) = Int(1/6*((108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(2/3)-12)/(108*b*x-108*a+12*(81*b^2*x^2-162*a*b*x+81*a^2+12)^(1/2))^(1/3),x)+_C1]