Internal problem ID [1083]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x^{4} y^{3}+y+\left (y^{2} x^{5}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 304
dsolve((x^4*y(x)^3+y(x))+(x^5*y(x)^2-x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}{2 x^{2}}+\frac {2 c_{1}}{x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}}{\sqrt {c_{1}}} \\ y \relax (x ) = \frac {-\frac {\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}{4 x^{2}}-\frac {c_{1}}{x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}\, \left (\frac {\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}{2 x^{2}}-\frac {2 c_{1}}{x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}\right )}{2}}{\sqrt {c_{1}}} \\ y \relax (x ) = \frac {-\frac {\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}{4 x^{2}}-\frac {c_{1}}{x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}{2 x^{2}}-\frac {2 c_{1}}{x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}}}\right )}{2}}{\sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.061 (sec). Leaf size: 267
DSolve[(x^4*y[x]^3+y[x])+(x^5*y[x]^2-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2+\frac {\sqrt [3]{2} \left (3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}\right ){}^{2/3}}{x^4}}{2^{2/3} \sqrt [3]{3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}}} \\ y(x)\to \frac {-2 \sqrt [3]{-2} x^4+(-2)^{2/3} \left (3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}\right ){}^{2/3}}{2 x^4 \sqrt [3]{3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}}} \\ y(x)\to \frac {2 (-1)^{2/3} x^4-\sqrt [3]{-2} \left (3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}\right ){}^{2/3}}{2^{2/3} x^4 \sqrt [3]{3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}}} \\ \end{align*}