Internal problem ID [5001]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 2, First order differential equations. Review problems. page 79
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 164
dsolve(t^3*y(t)^2+t^4/(y(t)^6)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) = \frac {1}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} y \left (t \right ) = \frac {-\cos \left (\frac {\pi }{7}\right )-i \cos \left (\frac {5 \pi }{14}\right )}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} y \left (t \right ) = \frac {-\cos \left (\frac {\pi }{7}\right )+i \cos \left (\frac {5 \pi }{14}\right )}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} y \left (t \right ) = \frac {\cos \left (\frac {2 \pi }{7}\right )-i \cos \left (\frac {3 \pi }{14}\right )}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} y \left (t \right ) = \frac {\cos \left (\frac {2 \pi }{7}\right )+i \cos \left (\frac {3 \pi }{14}\right )}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} y \left (t \right ) = \frac {-\cos \left (\frac {3 \pi }{7}\right )-i \cos \left (\frac {\pi }{14}\right )}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} y \left (t \right ) = \frac {-\cos \left (\frac {3 \pi }{7}\right )+i \cos \left (\frac {\pi }{14}\right )}{\left (c_{1} +7 \ln \left (t \right )\right )^{\frac {1}{7}}} \end{align*}
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 183
DSolve[t^3*y[t]^2+t^4/(y[t]^6)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {\sqrt [7]{-\frac {1}{7}}}{\sqrt [7]{\log (t)-c_1}} y(t)\to \frac {1}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}} y(t)\to \frac {(-1)^{2/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}} y(t)\to -\frac {(-1)^{3/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}} y(t)\to \frac {(-1)^{4/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}} y(t)\to -\frac {(-1)^{5/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}} y(t)\to \frac {(-1)^{6/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}} y(t)\to 0 \end{align*}