Internal problem ID [3734]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1017.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.102 (sec). Leaf size: 209
dsolve(diff(y(x),x)^3+x-y(x) = 0,y(x), singsol=all)
\begin{align*} x -\frac {3 \left (-x +y \relax (x )\right )^{\frac {2}{3}}}{2}-3 \left (-x +y \relax (x )\right )^{\frac {1}{3}}-3 \ln \left (\left (-x +y \relax (x )\right )^{\frac {1}{3}}-1\right )-c_{1} = 0 \\ x +\frac {3 \left (-x +y \relax (x )\right )^{\frac {2}{3}}}{4}-\frac {3 i \sqrt {3}\, \left (-x +y \relax (x )\right )^{\frac {2}{3}}}{4}+\frac {3 \left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}+\frac {3 i \sqrt {3}\, \left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}-3 \ln \left (-\frac {\left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}-1\right )-c_{1} = 0 \\ x +\frac {3 \left (-x +y \relax (x )\right )^{\frac {2}{3}}}{4}+\frac {3 i \sqrt {3}\, \left (-x +y \relax (x )\right )^{\frac {2}{3}}}{4}+\frac {3 \left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}-\frac {3 i \sqrt {3}\, \left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}-3 \ln \left (-\frac {\left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-x +y \relax (x )\right )^{\frac {1}{3}}}{2}-1\right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.947 (sec). Leaf size: 298
DSolve[(y'[x])^3 +x-y[x]==0 x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {3}{2} (y(x)-x)^{2/3}+3 \sqrt [3]{y(x)-x}+3 \log \left (\sqrt [3]{y(x)-x}-1\right )-x=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{2} \left (\frac {1}{2} \sqrt [3]{y(x)-x} \left (4 i (y(x)-x)^{2/3}+3 \sqrt {3} \sqrt [3]{y(x)-x}-3 i \sqrt [3]{y(x)-x}-6 \sqrt {3}-6 i\right )+6 i \log \left (\sqrt {2-2 i \sqrt {3}}-2 i \sqrt [3]{y(x)-x}\right )\right )-i (y(x)-x)=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {y(x)}{2}+\frac {1}{4} \left (-\frac {1}{2} \sqrt [3]{y(x)-x} \left (4 (y(x)-x)^{2/3}+3 i \sqrt {3} \sqrt [3]{y(x)-x}-3 \sqrt [3]{y(x)-x}-6 i \sqrt {3}-6\right )-6 \log \left (2 i \sqrt [3]{y(x)-x}+\sqrt {2+2 i \sqrt {3}}\right )\right )=c_1,y(x)\right ] \\ \end{align*}