Internal problem ID [4403]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 6
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
\[ \boxed {u^{\prime }+b u^{2}=\frac {c}{x^{4}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(u(x),x)+b*u(x)^2=c*x^(-4),u(x), singsol=all)
\[ u \left (x \right ) = \frac {-\sqrt {-b c}\, \tan \left (\frac {\sqrt {-b c}\, \left (c_{1} x -1\right )}{x}\right )+x}{b \,x^{2}} \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 98
DSolve[u'[x]+b*u[x]^2==x^(-4),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {-2 b c_1 e^{\frac {2 \sqrt {b}}{x}}+\sqrt {b} \left (1+2 c_1 x e^{\frac {2 \sqrt {b}}{x}}\right )+x}{x^2 \left (b+2 b^{3/2} c_1 e^{\frac {2 \sqrt {b}}{x}}\right )} \\ u(x)\to \frac {x-\sqrt {b}}{b x^2} \\ \end{align*}