Internal problem ID [4281]
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 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y^{2}}{x}-\frac {y}{x}+2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 15
dsolve(diff(y(x),x)= 2/x*y(x)^2+1/x*y(x)-2*x,y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (2 x +2 c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.677 (sec). Leaf size: 27
DSolve[y'[x]== 2/x*y[x]^2+1/x*y[x]-2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \tanh (2 x+c_1) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}