Internal problem ID [1028]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {3 y}{x}-\frac {3 y^{2} x^{4}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \relax (x ) = \frac {-5+\sqrt {48 x +1}}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.809 (sec). Leaf size: 37
DSolve[{y'[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]
\begin{align*} y(x)\to \frac {\sqrt {\frac {1}{x^2}} \sqrt {x^4 (48 x+1)}-5 x}{2 x^3} \\ \end{align*}