Internal problem ID [3894]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 6
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {u^{\prime }+u^{2}-\frac {c}{x^{\frac {4}{3}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve(diff(u(x),x)+u(x)^2=c*x^(-4/3),u(x), singsol=all)
\[ u \relax (x ) = \frac {3 c}{x^{\frac {1}{3}} \left (3 \sqrt {-c}\, x^{\frac {1}{3}} \tan \left (-3 x^{\frac {1}{3}} \sqrt {-c}+3 c_{1} \sqrt {-c}\right )-1\right )} \]
✓ Solution by Mathematica
Time used: 0.274 (sec). Leaf size: 156
DSolve[u'[x]+u[x]^2==c*x^(-4/3),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {3 c \left (c_1 \cosh \left (3 \sqrt {c} \sqrt [3]{x}\right )-i \sinh \left (3 \sqrt {c} \sqrt [3]{x}\right )\right )}{\sqrt [3]{x} \left (\left (-3 i \sqrt {c} \sqrt [3]{x}-c_1\right ) \cosh \left (3 \sqrt {c} \sqrt [3]{x}\right )+\left (3 \sqrt {c} c_1 \sqrt [3]{x}+i\right ) \sinh \left (3 \sqrt {c} \sqrt [3]{x}\right )\right )} \\ u(x)\to \frac {3 c}{\sqrt [3]{x} \left (3 \sqrt {c} \sqrt [3]{x} \tanh \left (3 \sqrt {c} \sqrt [3]{x}\right )-1\right )} \\ \end{align*}