Internal problem ID [3769]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1056.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {4 \left (y^{\prime }\right )^{3}+4 y^{\prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 198
dsolve(4*diff(y(x),x)^3+4*diff(y(x),x) = x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \int -\frac {i \left (\sqrt {3}\, \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}-i \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {2}{3}}+12 \sqrt {3}+12 i\right )}{12 \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \relax (x ) = \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 +c_{1} \\ y \relax (x ) = \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 +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 12.67 (sec). Leaf size: 362
DSolve[4 (y'[x])^3 +4 y'[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (-\frac {8 (-1)^{2/3} \sqrt [6]{3} \left (27 \sqrt {3} x^2-9 \sqrt {27 x^2+64} x+16 \sqrt {3}\right )}{\left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+\frac {\sqrt [3]{-3} \left (3 x \left (\sqrt {81 x^2+192}-9 x\right )+32\right )}{\left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}+24 c_1\right ) \\ y(x)\to \frac {\sqrt [3]{-1} \left (27 \sqrt {3} x^2-9 \sqrt {27 x^2+64} x+16 \sqrt {3}\right )}{3^{5/6} \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+\frac {\left (-\frac {1}{3}\right )^{2/3} \left (27 x^2-3 \sqrt {81 x^2+192} x-32\right )}{8 \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}+c_1 \\ y(x)\to \frac {\left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}{48\ 3^{2/3}}-\frac {8}{3^{2/3} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}+\frac {9 \sqrt [6]{3} x \left (\sqrt {27 x^2+64}-3 \sqrt {3} x\right )-16\ 3^{2/3}}{3 \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+c_1 \\ \end{align*}