Internal problem ID [2706]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 73.
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 {4 x^{3} y^{2}}{x^{4} y+2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.105 (sec). Leaf size: 49
dsolve(diff(y(x),x)=(4*x^3*y(x)^2)/(x^4*y(x)+2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {x^{4}}{2}-\frac {\sqrt {x^{8}+4 c_{1}}}{2}}{c_{1}} \\ y \relax (x ) = \frac {\frac {x^{4}}{2}+\frac {\sqrt {x^{8}+4 c_{1}}}{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 56
DSolve[y'[x]==(4*x^3*y[x]^2)/(x^4*y[x]+2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{-x^4+\sqrt {x^8+4 c_1}} \\ y(x)\to -\frac {2}{x^4+\sqrt {x^8+4 c_1}} \\ y(x)\to 0 \\ \end{align*}