18.1.15 problem Problem 14.17

Internal problem ID [3471]
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
Date solved : Monday, January 27, 2025 at 07:38:11 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 x^{2} y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.103 (sec). Leaf size: 37

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: 0.700 (sec). Leaf size: 53

DSolve[{x*(1-2*x^2*y[x])*D[y[x],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*}