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]
\[ \boxed {y^{3} x^{4}+y+\left (y^{2} x^{5}-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 242
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 \left (x \right ) &= \frac {\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {2}{3}}+4 c_{1}}{2 x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}} \sqrt {c_{1}}} \\ y \left (x \right ) &= \frac {-i \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {2}{3}} \sqrt {3}+4 i \sqrt {3}\, c_{1} -\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {2}{3}}-4 c_{1}}{4 x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}} \sqrt {c_{1}}} \\ y \left (x \right ) &= -\frac {-i \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {2}{3}} \sqrt {3}+4 i \sqrt {3}\, c_{1} +\left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {2}{3}}+4 c_{1}}{4 x^{2} \left (4 x^{3}+4 \sqrt {x^{6}-4 c_{1}^{3}}\right )^{\frac {1}{3}} \sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 39.244 (sec). Leaf size: 300
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 {i \left (\left (\sqrt {3}+i\right ) \left (6 c_1 x^9+2 \sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}\right ){}^{2/3}-2 \sqrt [3]{2} \left (\sqrt {3}-i\right ) x^4\right )}{4 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 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) x^4+\left (-1-i \sqrt {3}\right ) \left (6 c_1 x^9+2 \sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}\right ){}^{2/3}}{4 x^4 \sqrt [3]{3 c_1 x^9+\sqrt {x^{12} \left (-4+9 c_1{}^2 x^6\right )}}} \\ \end{align*}