Internal problem ID [4404]
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]]
\[ \boxed {u^{\prime }-u^{2}=\frac {2}{x^{\frac {8}{3}}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 78
dsolve(diff(u(x),x)-u(x)^2=2*x^(-8/3),u(x), singsol=all)
\[ u \left (x \right ) = -\frac {3 \left (\tan \left (3 \sqrt {2}\, \left (\left (\frac {1}{x}\right )^{\frac {1}{3}}-c_{1} \right )\right ) \sqrt {2}\, x \left (\frac {1}{x}\right )^{\frac {2}{3}}+\frac {x \left (\frac {1}{x}\right )^{\frac {1}{3}}}{3}-2\right )}{\left (\frac {1}{x}\right )^{\frac {1}{3}} x^{2} \left (3 \left (\frac {1}{x}\right )^{\frac {1}{3}} \sqrt {2}\, \tan \left (3 \sqrt {2}\, \left (\left (\frac {1}{x}\right )^{\frac {1}{3}}-c_{1} \right )\right )+1\right )} \]
✓ Solution by Mathematica
Time used: 0.266 (sec). Leaf size: 215
DSolve[u'[x]-u[x]^2==x^(-8/3),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to -\frac {\left (-9 \sqrt [3]{\frac {1}{x}}+c_1 \left (8-24 \left (\frac {1}{x}\right )^{2/3}\right )\right ) \cos \left (3 \sqrt [3]{\frac {1}{x}}\right )+3 \left (-3 \left (\frac {1}{x}\right )^{2/3}+8 c_1 \sqrt [3]{\frac {1}{x}}+1\right ) \sin \left (3 \sqrt [3]{\frac {1}{x}}\right )}{x \left (\left (-9 \sqrt [3]{\frac {1}{x}}+8 c_1\right ) \cos \left (3 \sqrt [3]{\frac {1}{x}}\right )+3 \left (1+8 c_1 \sqrt [3]{\frac {1}{x}}\right ) \sin \left (3 \sqrt [3]{\frac {1}{x}}\right )\right )} \\ u(x)\to \frac {\left (3 \left (\frac {1}{x}\right )^{2/3}-1\right ) \cos \left (3 \sqrt [3]{\frac {1}{x}}\right )-3 \sqrt [3]{\frac {1}{x}} \sin \left (3 \sqrt [3]{\frac {1}{x}}\right )}{x \left (3 \sqrt [3]{\frac {1}{x}} \sin \left (3 \sqrt [3]{\frac {1}{x}}\right )+\cos \left (3 \sqrt [3]{\frac {1}{x}}\right )\right )} \\ \end{align*}