Internal problem ID [4402]
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]]
\[ \boxed {u^{\prime }+u^{2}=\frac {c}{x^{\frac {4}{3}}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(u(x),x)+u(x)^2=c*x^(-4/3),u(x), singsol=all)
\[ u \left (x \right ) = -\frac {3 c}{x^{\frac {1}{3}} \left (3 x^{\frac {1}{3}} \tan \left (3 \sqrt {-c}\, \left (x^{\frac {1}{3}}-c_{1} \right )\right ) \sqrt {-c}+1\right )} \]
✓ Solution by Mathematica
Time used: 0.286 (sec). Leaf size: 183
DSolve[u'[x]+u[x]^2==c*x^(-4/3),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {3 c \left (3 i \sinh \left (3 \sqrt {c} \sqrt [3]{x}\right )+8 c_1 \cosh \left (3 \sqrt {c} \sqrt [3]{x}\right )\right )}{\sqrt [3]{x} \left (\left (9 i \sqrt {c} \sqrt [3]{x}-8 c_1\right ) \cosh \left (3 \sqrt {c} \sqrt [3]{x}\right )+3 \left (8 \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 \cosh \left (3 \sqrt {c} \sqrt [3]{x}\right )}{\sqrt [3]{x} \left (\cosh \left (3 \sqrt {c} \sqrt [3]{x}\right )-3 \sqrt {c} \sqrt [3]{x} \sinh \left (3 \sqrt {c} \sqrt [3]{x}\right )\right )} \\ \end{align*}