Internal problem ID [4222]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter IX, Special forms of differential equations. Examples XVII. page 247
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {y^{\prime }+y^{2}-\frac {a^{2}}{x^{4}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x)+y(x)^2=a^2/x^4,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {-a^{2}}\, \tan \left (\frac {\sqrt {-a^{2}}\, \left (c_{1} x -1\right )}{x}\right )-x}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.312 (sec). Leaf size: 46
DSolve[y'[x]+y[x]^2==a^2/x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+a \left (-1+\frac {1}{\frac {1}{2}+a c_1 e^{\frac {2 a}{x}}}\right )}{x^2} \\ y(x)\to \frac {x-a}{x^2} \\ \end{align*}