29.9.6 problem 246

Internal problem ID [4846]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 246
Date solved : Monday, January 27, 2025 at 09:42:32 AM
CAS classification : [_rational, _Riccati]

\begin{align*} 3 x y^{\prime }&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(3*x*diff(y(x),x) = 3*x^(2/3)+(1-3*y(x))*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = i \tan \left (-3 i x^{{1}/{3}}+c_{1} \right ) x^{{1}/{3}} \]

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 79

DSolve[3 x D[y[x],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*}