12.5.53 problem 52

Internal problem ID [1677]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 52
Date solved : Monday, January 27, 2025 at 05:25:02 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 x^{2} y^{2}+6 y x +2}{x^{2} \left (2 y x +3\right )} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 18

dsolve([diff(y(x),x)+2/x*y(x)=(3*x^2*y(x)^2+6*x*y(x)+2)/(x^2*(2*x*y(x)+3)),y(2) = 2],y(x), singsol=all)
 

\[ y = \frac {-3+\sqrt {60 x +1}}{2 x} \]

✓ Solution by Mathematica

Time used: 0.736 (sec). Leaf size: 35

DSolve[{D[y[x],x]+2/x*y[x]==(3*x^2*y[x]^2+6*x*y[x]+2)/(x^2*(2*x*y[x]+3)),y[2]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {\frac {1}{x^2}} \sqrt {x^2 (60 x+1)}-3}{2 x} \]