Internal problem ID [4280]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 25 part (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} x +\frac {2 y}{x}+\frac {1}{x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 15
dsolve(diff(y(x),x)= x*y(x)^2-2/x*y(x)-1/x^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tanh \left (-\ln \relax (x )+c_{1}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.417 (sec). Leaf size: 63
DSolve[y'[x]== x*y[x]^2-2/x*y[x]-1/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \tan (i \log (x)+c_1)}{x^2} \\ y(x)\to \frac {-x^2+e^{2 i \text {Interval}[\{0,\pi \}]}}{x^4+x^2 e^{2 i \text {Interval}[\{0,\pi \}]}} \\ \end{align*}