28.1.70 problem 73

Internal problem ID [4376]
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
Date solved : Monday, January 27, 2025 at 09:09:31 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {4 x^{3} y^{2}}{x^{4} y+2} \end{align*}

✓ Solution by Maple

Time used: 0.738 (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: 0.422 (sec). Leaf size: 56

DSolve[D[y[x],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*}