28.1.23 problem 23

Internal problem ID [4329]
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 : 23
Date solved : Monday, January 27, 2025 at 09:03:24 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 67

dsolve((3*y(x)*(x^2-1))+(x^3+8*y(x)-3*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {x^{3}}{8}+\frac {3 x}{8}-\frac {\sqrt {x^{6}-6 x^{4}+9 x^{2}-16 c_{1}}}{8} \\ y \left (x \right ) &= -\frac {x^{3}}{8}+\frac {3 x}{8}+\frac {\sqrt {x^{6}-6 x^{4}+9 x^{2}-16 c_{1}}}{8} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 86

DSolve[(3*y[x]*(x^2-1))+(x^3+8*y[x]-3*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (-x^3-\sqrt {x^6-6 x^4+9 x^2+64 c_1}+3 x\right ) \\ y(x)\to \frac {1}{8} \left (-x^3+\sqrt {x^6-6 x^4+9 x^2+64 c_1}+3 x\right ) \\ y(x)\to 0 \\ \end{align*}