35.4.14 problem 25 part (a)

Internal problem ID [6132]
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)
Date solved : Monday, January 27, 2025 at 01:37:58 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(diff(y(x),x)= x*y(x)^2-2/x*y(x)-1/x^3,y(x), singsol=all)
 

\[ y = \frac {\tanh \left (-\ln \left (x \right )+c_1 \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 1.198 (sec). Leaf size: 63

DSolve[D[y[x],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*}