Internal problem ID [2500]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page
490
Problem number: Problem 14.17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x \left (1-2 y x^{2}\right ) y^{\prime }+y-3 y^{2} x^{2}=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 35
dsolve([x*(1-2*x^2*y(x))*diff(y(x),x) +y(x) = 3*x^2*y(x)^2,y(1) = 1/2],y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1-\sqrt {1-x}}{2 x^{2}} y \left (x \right ) = \frac {1+\sqrt {1-x}}{2 x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.599 (sec). Leaf size: 53
DSolve[{x*(1-2*x^2*y[x])*y'[x] +y[x] == 3*x^2*y[x]^2,y[1]==1/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-\sqrt {-\left ((x-1) x^2\right )}}{2 x^3} y(x)\to \frac {\sqrt {-\left ((x-1) x^2\right )}+x}{2 x^3} \end{align*}