Internal problem ID [4240]
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]
\[ \boxed {{y^{\prime }}^{3}=b x +a} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 66
dsolve(diff(y(x),x)^3 = b*x+a,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {3 \left (x b +a \right )^{\frac {4}{3}}}{4 b}+c_{1} y \left (x \right ) = -\frac {3 i \left (x b +a \right )^{\frac {4}{3}} \left (-i+\sqrt {3}\right )}{8 b}+c_{1} y \left (x \right ) = \frac {3 i \left (x b +a \right )^{\frac {4}{3}} \left (\sqrt {3}+i\right )}{8 b}+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (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*}