Internal problem ID [14304]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational]
\[ \boxed {-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(-1/y(t)+(t/y(t)^2+3*y(t)^2)*diff(y(t),t)=0,y(t), singsol=all)
\[ -y \left (t \right )^{4}-c_{1} y \left (t \right )+t = 0 \]
✓ Solution by Mathematica
Time used: 60.122 (sec). Leaf size: 1073
DSolve[-1/y[t]+(t/y[t]^2+3*y[t]^2)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}{2 \sqrt [3]{6}}-\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{\frac {2}{3}} t}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}{\sqrt [3]{2} 3^{2/3}}-\frac {2 \sqrt [3]{6} c_1}{\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}} \\ y(t)\to \frac {\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}{2 \sqrt [3]{6}}+\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{\frac {2}{3}} t}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}{\sqrt [3]{2} 3^{2/3}}-\frac {2 \sqrt [3]{6} c_1}{\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}} \\ y(t)\to -\frac {\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}{2 \sqrt [3]{6}}-\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{\frac {2}{3}} t}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}{\sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{6} c_1}{\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}} \\ y(t)\to \frac {1}{2} \sqrt {\frac {4 \sqrt [3]{\frac {2}{3}} t}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}{\sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{6} c_1}{\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}}-\frac {\sqrt {\frac {-8 \sqrt [3]{3} t+\sqrt [3]{2} \left (9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}\right ){}^{2/3}}{\sqrt [3]{9 c_1{}^2-\sqrt {768 t^3+81 c_1{}^4}}}}}{2 \sqrt [3]{6}} \\ \end{align*}