Internal problem ID [3732]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1015.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-b x -a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.107 (sec). Leaf size: 68
dsolve(diff(y(x),x)^3 = b*x+a,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3 \left (b x +a \right )^{\frac {4}{3}}}{4 b}+c_{1} \\ y \relax (x ) = \frac {3 i \left (b x +a \right )^{\frac {4}{3}} \left (i-\sqrt {3}\right )}{8 b}+c_{1} \\ y \relax (x ) = \frac {3 i \left (b x +a \right )^{\frac {4}{3}} \left (\sqrt {3}+i\right )}{8 b}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 80
DSolve[(y'[x])^3 ==a+b x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 (a+b x)^{4/3}}{4 b}+c_1 \\ y(x)\to -\frac {3 \sqrt [3]{-1} (a+b x)^{4/3}}{4 b}+c_1 \\ y(x)\to \frac {3 (-1)^{2/3} (a+b x)^{4/3}}{4 b}+c_1 \\ \end{align*}