Internal problem ID [3502]
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]
\[ \boxed {3 x y^{\prime }-\left (1-3 y\right ) y=3 x^{\frac {2}{3}}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = i \tan \left (-3 i x^{\frac {1}{3}}+c_{1} \right ) x^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.181 (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*}