Internal problem ID [1991]
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]]
Solve \begin {gather*} \boxed {x \left (-2 y x^{2}+1\right ) y^{\prime }+y-3 x^{2} y^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.065 (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 \relax (x ) = \frac {1-\sqrt {1-x}}{2 x^{2}} \\ y \relax (x ) = \frac {1+\sqrt {1-x}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.429 (sec). Leaf size: 50
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 {1}{2 \left (\sqrt {-\left ((x-1) x^2\right )}+x\right )} \\ y(x)\to \frac {\sqrt {-\left ((x-1) x^2\right )}+x}{2 x^3} \\ \end{align*}