Internal problem ID [3215]
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`]]
\[ \boxed {y^{\prime }-\frac {4 x^{3} y^{2}}{y x^{4}+2}=0} \]
✓ Solution by Maple
Time used: 0.594 (sec). Leaf size: 45
dsolve(diff(y(x),x)=(4*x^3*y(x)^2)/(x^4*y(x)+2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{4}-\sqrt {x^{8}+4 c_{1}}}{2 c_{1}} \\ y \left (x \right ) &= \frac {x^{4}+\sqrt {x^{8}+4 c_{1}}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.409 (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*}