Internal problem ID [3739]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1022.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+y^{\prime }+a -b x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 335
dsolve(diff(y(x),x)^3+diff(y(x),x)+a-b*x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \int \frac {i \left (i \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +81 a^{2}+12}\right )^{\frac {2}{3}}-\left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +81 a^{2}+12}\right )^{\frac {2}{3}} \sqrt {3}-12 i-12 \sqrt {3}\right )}{12 \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \relax (x ) = \int \frac {i \left (\left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +81 a^{2}+12}\right )^{\frac {2}{3}} \sqrt {3}+12 \sqrt {3}+i \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +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 b x a +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \relax (x ) = \int \frac {\left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +81 a^{2}+12}\right )^{\frac {2}{3}}-12}{6 \left (108 b x -108 a +12 \sqrt {81 b^{2} x^{2}-162 b x a +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 22.588 (sec). Leaf size: 740
DSolve[(y'[x])^3 +y'[x]+a-b x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-9 \sqrt [3]{2} \sqrt [6]{3} \sqrt {27 (a-b x)^2+4} \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x\right )^{2/3} (a-b x)+27\ 2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x} (a-b x)+\sqrt [3]{2} 3^{2/3} \left (27 (a-b x)^2-2\right ) \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt {27 (a-b x)^2+4} \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x}+144 b c_1}{144 b} \\ y(x)\to \frac {-9 (-1)^{2/3} \sqrt [3]{2} \sqrt [6]{3} \sqrt {27 (a-b x)^2+4} \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x\right )^{2/3} (a-b x)-27 \sqrt [3]{-3} 2^{2/3} \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x} (a-b x)+(-3)^{2/3} \sqrt [3]{2} \left (27 (a-b x)^2-2\right ) \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x\right )^{2/3}+\sqrt [3]{-1} 2^{2/3} 3^{5/6} \sqrt {27 (a-b x)^2+4} \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x}+144 b c_1}{144 b} \\ y(x)\to \frac {1}{144} \left (\frac {\sqrt [3]{-2} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x} \left (9 \sqrt {27 (a-b x)^2+4} \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x} (a-b x)+27 \sqrt [3]{-2} \sqrt [6]{3} (a-b x)-\sqrt [3]{-2} 3^{2/3} \sqrt {27 (a-b x)^2+4}+\sqrt {3} \left (2-27 (a-b x)^2\right ) \sqrt [3]{\sqrt {3} \sqrt {27 (a-b x)^2+4}+9 a-9 b x}\right )}{b}+144 c_1\right ) \\ \end{align*}