12.5.54 problem 53

Internal problem ID [1678]
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 : 53
Date solved : Monday, January 27, 2025 at 05:25:10 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }+\frac {3 y}{x}&=\frac {3 x^{4} y^{2}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 18

dsolve([diff(y(x),x)+3/x*y(x)=(3*x^4*y(x)^2+10*x^2*y(x)+6)/(x^3*(2*x^2*y(x)+5)),y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {-5+\sqrt {48 x +1}}{2 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.884 (sec). Leaf size: 37

DSolve[{D[y[x],x]+3/x*y[x]==(3*x^4*y[x]^2+10*x^2*y[x]+6)/(x^3*(2*x^2*y[x]+5)),y[1]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {\frac {1}{x^2}} \sqrt {x^4 (48 x+1)}-5 x}{2 x^3} \]