1.23 problem 23

Internal problem ID [2659]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class A]]

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

Solution by Maple

Time used: 0.002 (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 \relax (x ) = -\frac {x^{3}}{8}+\frac {3 x}{8}-\frac {\sqrt {x^{6}-6 x^{4}+9 x^{2}-16 c_{1}}}{8} \\ y \relax (x ) = -\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: 0.114 (sec). Leaf size: 82

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

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