Internal problem ID [1054]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {x^{3} y^{4}+x +\left (x^{4} y^{3}+y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 111
dsolve((x^3*y(x)^4+x)+(x^4*y(x)^3+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-1-\sqrt {-2 x^{6}-4 x^{4} c_{1}+1}}}{x^{2}} \\ y \relax (x ) = \frac {\sqrt {-1+\sqrt {-2 x^{6}-4 x^{4} c_{1}+1}}}{x^{2}} \\ y \relax (x ) = -\frac {\sqrt {-1-\sqrt {-2 x^{6}-4 x^{4} c_{1}+1}}}{x^{2}} \\ y \relax (x ) = -\frac {\sqrt {-1+\sqrt {-2 x^{6}-4 x^{4} c_{1}+1}}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.772 (sec). Leaf size: 135
DSolve[(x^3*y[x]^4+x)+(x^4*y[x]^3+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {1+\sqrt {-2 x^6+4 c_1 x^4+1}}{x^4}} \\ y(x)\to \sqrt {-\frac {1+\sqrt {-2 x^6+4 c_1 x^4+1}}{x^4}} \\ y(x)\to -\sqrt {\frac {-1+\sqrt {-2 x^6+4 c_1 x^4+1}}{x^4}} \\ y(x)\to \sqrt {\frac {-1+\sqrt {-2 x^6+4 c_1 x^4+1}}{x^4}} \\ \end{align*}