Internal problem ID [14180]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(t),t)=t^3/(y(t)*sqrt((1-y(t)^2)*(t^4+9))),y(t), singsol=all)
\[ -\left (-\frac {y \left (t \right )^{2}}{3}+\int _{}^{t}\frac {\textit {\_a}^{3}}{\sqrt {-\left (\textit {\_a}^{4}+9\right ) \left (y \left (t \right )^{2}-1\right )}}d \textit {\_a} +\frac {1}{3}\right ) \sqrt {y \left (t \right )+1}\, \sqrt {-1+y \left (t \right )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.286 (sec). Leaf size: 519
DSolve[y'[t]==t^3/(y[t]*Sqrt[(1-y[t]^2)*(t^4+9)]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {1+\left (\frac {3}{2}\right )^{2/3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}} \\ y(t)\to \sqrt {1+\left (\frac {3}{2}\right )^{2/3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}} \\ y(t)\to -\frac {1}{2} \sqrt {-\sqrt [3]{2} 3^{2/3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}-3 i \sqrt [3]{2} \sqrt [6]{3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}+4} \\ y(t)\to \frac {1}{2} \sqrt {-\sqrt [3]{2} 3^{2/3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}-3 i \sqrt [3]{2} \sqrt [6]{3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}+4} \\ y(t)\to -\frac {1}{2} \sqrt {-\sqrt [3]{2} 3^{2/3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}+3 i \sqrt [3]{2} \sqrt [6]{3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}+4} \\ y(t)\to \frac {1}{2} \sqrt {-\sqrt [3]{2} 3^{2/3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}+3 i \sqrt [3]{2} \sqrt [6]{3} \sqrt [3]{-t^4-4 i c_1 \sqrt {t^4+9}-9+4 c_1{}^2}+4} \\ \end{align*}