Internal problem ID [6328]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }-y+y^{2}-x^{\frac {2}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 85
dsolve(x*diff(y(x),x)-y(x)+y(x)^2=x^(2/3),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (\left (-{| 3 x^{\frac {1}{3}}-1|} c_{1}-\mathrm {abs}\left (1, 3 x^{\frac {1}{3}}-1\right ) c_{1}\right ) {\mathrm e}^{3 x^{\frac {1}{3}}}+3 \,{\mathrm e}^{-3 x^{\frac {1}{3}}} x^{\frac {1}{3}}\right ) x^{\frac {1}{3}}}{c_{1} {\mathrm e}^{3 x^{\frac {1}{3}}} {| 3 x^{\frac {1}{3}}-1|}+\left (3 x^{\frac {1}{3}}+1\right ) {\mathrm e}^{-3 x^{\frac {1}{3}}}} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 103
DSolve[x*y'[x]-y[x]+y[x]^2==x^(2/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x^{2/3}}{3 i c_1 \sqrt [3]{x}+\frac {3 \left (1+c_1{}^2\right ) \sqrt [3]{x} \cosh \left (3 \sqrt [3]{x}\right )}{\sinh \left (3 \sqrt [3]{x}\right )+i c_1 \cosh \left (3 \sqrt [3]{x}\right )}-1} \\ y(x)\to \frac {3 x^{2/3}}{3 \sqrt [3]{x} \tanh \left (3 \sqrt [3]{x}\right )-1} \\ \end{align*}