Internal problem ID [3733]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1016.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-a \,x^{n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 77
dsolve(diff(y(x),x)^3 = a*x^n,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3 x \left (a \,x^{n}\right )^{\frac {1}{3}}}{n +3}+c_{1} \\ y \relax (x ) = \frac {3 x \left (-1+i \sqrt {3}\right ) \left (a \,x^{n}\right )^{\frac {1}{3}}}{2 \left (n +3\right )}+c_{1} \\ y \relax (x ) = -\frac {3 x \left (1+i \sqrt {3}\right ) \left (a \,x^{n}\right )^{\frac {1}{3}}}{2 \left (n +3\right )}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 95
DSolve[(y'[x])^3 ==a x^n,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 \sqrt [3]{a} x^{\frac {n}{3}+1}}{n+3}+c_1 \\ y(x)\to -\frac {3 \sqrt [3]{-1} \sqrt [3]{a} x^{\frac {n}{3}+1}}{n+3}+c_1 \\ y(x)\to \frac {3 (-1)^{2/3} \sqrt [3]{a} x^{\frac {n}{3}+1}}{n+3}+c_1 \\ \end{align*}