Internal problem ID [3768]
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]
\[ \boxed {4 {y^{\prime }}^{3}+4 y^{\prime }-x=0} \]
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 198
dsolve(4*diff(y(x),x)^3+4*diff(y(x),x) = x,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \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 \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 +c_{1} \\ 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 +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.005 (sec). Leaf size: 360
DSolve[4 (y'[x])^3 +4 y'[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-\frac {1}{3}} \left (27 x^2-3 \sqrt {81 x^2+192} x+16\right )}{\left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+\frac {\left (1-i \sqrt {3}\right ) \left (3 x \left (\sqrt {81 x^2+192}-9 x\right )+32\right )}{16\ 3^{2/3} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}}+c_1 \\ y(x)\to \frac {i \left (\sqrt {3}+i\right ) \left (3 x \left (\sqrt {81 x^2+192}-9 x\right )-16\right )}{2 \sqrt [3]{3} \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+\frac {\left (1+i \sqrt {3}\right ) \left (3 x \left (\sqrt {81 x^2+192}-9 x\right )+32\right )}{16\ 3^{2/3} \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*}