Internal problem ID [14408]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\left (2 y^{4}-6 y^{9}\right ) y^{\prime }=\frac {1}{x^{5}}-\frac {1}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 530
dsolve((-x^(-5)+x^(-3))=(2*y(x)^4-6*y(x)^9)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {6^{\frac {4}{5}} \left (2 x^{5}+x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{6 x} \\ y \left (x \right ) &= \frac {6^{\frac {4}{5}} \left (2 x^{5}-x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{6 x} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {10-2 \sqrt {5}}+\sqrt {5}+1\right ) 6^{\frac {4}{5}} \left (2 x^{5}+x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= \frac {\left (i \sqrt {10-2 \sqrt {5}}-\sqrt {5}-1\right ) 6^{\frac {4}{5}} \left (2 x^{5}+x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {10+2 \sqrt {5}}-\sqrt {5}+1\right ) 6^{\frac {4}{5}} \left (2 x^{5}+x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= \frac {\left (i \sqrt {10+2 \sqrt {5}}+\sqrt {5}-1\right ) 6^{\frac {4}{5}} \left (2 x^{5}+x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {10-2 \sqrt {5}}+\sqrt {5}+1\right ) 6^{\frac {4}{5}} \left (2 x^{5}-x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= \frac {\left (i \sqrt {10-2 \sqrt {5}}-\sqrt {5}-1\right ) 6^{\frac {4}{5}} \left (2 x^{5}-x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {10+2 \sqrt {5}}-\sqrt {5}+1\right ) 6^{\frac {4}{5}} \left (2 x^{5}-x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ y \left (x \right ) &= \frac {\left (i \sqrt {10+2 \sqrt {5}}+\sqrt {5}-1\right ) 6^{\frac {4}{5}} \left (2 x^{5}-x^{3} \sqrt {-60 c_{1} x^{4}+30 x^{2}-15}\right )^{\frac {1}{5}}}{24 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 16.779 (sec). Leaf size: 409
DSolve[(-x^(-5)+x^(-3))==(2*y[x]^4-6*y[x]^9)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [5]{2-\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to -\sqrt [5]{-\frac {1}{6}} \sqrt [5]{2-\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}} \\ y(x)\to \frac {(-1)^{2/5} \sqrt [5]{2-\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to -\frac {(-1)^{3/5} \sqrt [5]{2-\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to \frac {(-1)^{4/5} \sqrt [5]{2-\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to \frac {\sqrt [5]{2+\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to -\sqrt [5]{-\frac {1}{6}} \sqrt [5]{2+\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}} \\ y(x)\to \frac {(-1)^{2/5} \sqrt [5]{2+\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to -\frac {(-1)^{3/5} \sqrt [5]{2+\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ y(x)\to \frac {(-1)^{4/5} \sqrt [5]{2+\sqrt {-\frac {15}{x^4}+\frac {30}{x^2}+4+120 c_1}}}{\sqrt [5]{6}} \\ \end{align*}