Internal problem ID [3896]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 6
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {u^{\prime }-u^{2}-\frac {2}{x^{\frac {8}{3}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 85
dsolve(diff(u(x),x)-u(x)^2=2*x^(-8/3),u(x), singsol=all)
\[ u \relax (x ) = -\frac {3 \tan \left (-3 \left (\frac {1}{x}\right )^{\frac {1}{3}} \sqrt {2}+3 \sqrt {2}\, c_{1}\right ) \sqrt {2}\, x \left (\frac {1}{x}\right )^{\frac {2}{3}}-x \left (\frac {1}{x}\right )^{\frac {1}{3}}+6}{\left (\frac {1}{x}\right )^{\frac {1}{3}} x^{2} \left (3 \sqrt {2}\, \left (\frac {1}{x}\right )^{\frac {1}{3}} \tan \left (-3 \left (\frac {1}{x}\right )^{\frac {1}{3}} \sqrt {2}+3 \sqrt {2}\, c_{1}\right )-1\right )} \]
✓ Solution by Mathematica
Time used: 0.267 (sec). Leaf size: 143
DSolve[u'[x]-u[x]^2==x^(-8/3),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {\left (-x^{2/3}+3 c_1 \sqrt [3]{x}+3\right ) \cos \left (\frac {3}{\sqrt [3]{x}}\right )-\left (3 \sqrt [3]{x}+c_1 \left (x^{2/3}-3\right )\right ) \sin \left (\frac {3}{\sqrt [3]{x}}\right )}{x^{4/3} \left (\left (\sqrt [3]{x}-3 c_1\right ) \cos \left (\frac {3}{\sqrt [3]{x}}\right )+\left (3+c_1 \sqrt [3]{x}\right ) \sin \left (\frac {3}{\sqrt [3]{x}}\right )\right )} \\ u(x)\to \frac {3}{x^{5/3}-3 x^{4/3} \cot \left (\frac {3}{\sqrt [3]{x}}\right )}-\frac {1}{x} \\ \end{align*}