Internal problem ID [2994]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 246.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {3 y^{\prime } x -3 x^{\frac {2}{3}}-\left (-3 y+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(3*x*diff(y(x),x) = 3*x^(2/3)+(1-3*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = i \tan \left (-3 i x^{\frac {1}{3}}+c_{1}\right ) x^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 79
DSolve[3 x y'[x]==3 x^(2/3)+(1-3 y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x} \left (i \cosh \left (3 \sqrt [3]{x}\right )+c_1 \sinh \left (3 \sqrt [3]{x}\right )\right )}{i \sinh \left (3 \sqrt [3]{x}\right )+c_1 \cosh \left (3 \sqrt [3]{x}\right )} \\ y(x)\to \sqrt [3]{x} \tanh \left (3 \sqrt [3]{x}\right ) \\ \end{align*}