Internal problem ID [3738]
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]
\[ \boxed {{y^{\prime }}^{3}+y^{\prime }+a -b x=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 334
dsolve(diff(y(x),x)^3+diff(y(x),x)+a-b*x = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \int -\frac {i \left (\sqrt {3}\, \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {2}{3}}-i \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {2}{3}}+12 \sqrt {3}+12 i\right )}{12 \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \left (x \right ) = \int \frac {i \left (\sqrt {3}\, \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {2}{3}}+12 \sqrt {3}+i \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {2}{3}}-12 i\right )}{12 \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \left (x \right ) = \int \frac {\left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {2}{3}}-12}{6 \left (108 x b -108 a +12 \sqrt {81 b^{2} x^{2}-162 x b a +81 a^{2}+12}\right )^{\frac {1}{3}}}d x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.013 (sec). Leaf size: 667
DSolve[(y'[x])^3 +y'[x]+a-b x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{144} \left (\frac {2^{2/3} \sqrt [3]{3} \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{4/3}}{b}-\frac {4 \sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{2/3}}{b}-\frac {24\ 2^{2/3} \sqrt [3]{3}}{b \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{2/3}}+\frac {24 \sqrt [3]{2} 3^{2/3}}{b \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{4/3}}+144 c_1\right ) \\ y(x)\to \frac {1}{288} \left (\frac {i 2^{2/3} \sqrt [3]{3} \left (\sqrt {3}+i\right ) \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{4/3}}{b}+\frac {4 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{2/3}}{b}-\frac {48 (-2)^{2/3} \sqrt [3]{3}}{b \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{2/3}}-\frac {48 \sqrt [3]{-2} 3^{2/3}}{b \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{4/3}}+288 c_1\right ) \\ y(x)\to \frac {1}{288} \left (-\frac {i 2^{2/3} \sqrt [3]{3} \left (\sqrt {3}-i\right ) \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{4/3}}{b}+\frac {4 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{2/3}}{b}+\frac {48 \sqrt [3]{-3} 2^{2/3}}{b \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{2/3}}+\frac {48 (-3)^{2/3} \sqrt [3]{2}}{b \left (\sqrt {3} \sqrt {27 (a-b x)^2+4}-9 a+9 b x\right )^{4/3}}+288 c_1\right ) \\ \end{align*}