Internal problem ID [3421]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 165.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x y^{\prime }-y+y^{2}=x^{\frac {2}{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 85
dsolve(x*diff(y(x),x)-y(x)+y(x)^2 = x^(2/3),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (-{| 3 x^{\frac {1}{3}}-1|} c_{1} -\operatorname {abs}\left (1, 3 x^{\frac {1}{3}}-1\right ) c_{1} \right ) {\mathrm e}^{3 x^{\frac {1}{3}}}+3 \,{\mathrm e}^{-3 x^{\frac {1}{3}}} x^{\frac {1}{3}}\right ) x^{\frac {1}{3}}}{c_{1} {\mathrm e}^{3 x^{\frac {1}{3}}} {| 3 x^{\frac {1}{3}}-1|}+\left (3 x^{\frac {1}{3}}+1\right ) {\mathrm e}^{-3 x^{\frac {1}{3}}}} \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 131
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} \left (c_1 \cosh \left (3 \sqrt [3]{x}\right )-i \sinh \left (3 \sqrt [3]{x}\right )\right )}{\left (-3 i \sqrt [3]{x}-c_1\right ) \cosh \left (3 \sqrt [3]{x}\right )+\left (3 c_1 \sqrt [3]{x}+i\right ) \sinh \left (3 \sqrt [3]{x}\right )} y(x)\to \frac {3 x^{2/3} \cosh \left (3 \sqrt [3]{x}\right )}{3 \sqrt [3]{x} \sinh \left (3 \sqrt [3]{x}\right )-\cosh \left (3 \sqrt [3]{x}\right )} \end{align*}