Internal problem ID [1056]
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: 27(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {x^{3} y^{4}+2 x +\left (x^{4} y^{3}+3 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 111
dsolve((x^3*y(x)^4+2*x)+(x^4*y(x)^3+3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-3-\sqrt {-4 x^{6}-4 x^{4} c_{1}+9}}}{x^{2}} \\ y \relax (x ) = \frac {\sqrt {-3+\sqrt {-4 x^{6}-4 x^{4} c_{1}+9}}}{x^{2}} \\ y \relax (x ) = -\frac {\sqrt {-3-\sqrt {-4 x^{6}-4 x^{4} c_{1}+9}}}{x^{2}} \\ y \relax (x ) = -\frac {\sqrt {-3+\sqrt {-4 x^{6}-4 x^{4} c_{1}+9}}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.494 (sec). Leaf size: 135
DSolve[(x^3*y[x]^4+2*x)+(x^4*y[x]^3+3*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {3+\sqrt {-4 x^6+4 c_1 x^4+9}}{x^4}} \\ y(x)\to \sqrt {-\frac {3+\sqrt {-4 x^6+4 c_1 x^4+9}}{x^4}} \\ y(x)\to -\sqrt {\frac {-3+\sqrt {-4 x^6+4 c_1 x^4+9}}{x^4}} \\ y(x)\to \sqrt {\frac {-3+\sqrt {-4 x^6+4 c_1 x^4+9}}{x^4}} \\ \end{align*}