Internal problem ID [14400]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {t^{\frac {1}{3}} y^{\frac {2}{3}}+\left (t^{\frac {2}{3}} y^{\frac {1}{3}}+y\right ) y^{\prime }=-t} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 171
dsolve((t^(1/3)*y(t)^(2/3)+t)+(t^(2/3)*y(t)^(1/3)+y(t))*diff(y(t),t)=0,y(t), singsol=all)
\[ -\left (\int _{\textit {\_b}}^{t}\frac {y \left (t \right )^{\frac {8}{3}} \textit {\_a}^{\frac {1}{3}}-y \left (t \right )^{\frac {4}{3}} \textit {\_a}^{\frac {5}{3}}+\textit {\_a}^{3}}{\textit {\_a}^{4}+y \left (t \right )^{4}}d \textit {\_a} \right )-\frac {\left (\int _{}^{y \left (t \right )}\frac {\left (4 t^{2}+4 \textit {\_f}^{\frac {2}{3}} t^{\frac {4}{3}}+4 \textit {\_f}^{\frac {4}{3}} t^{\frac {2}{3}}+4 \textit {\_f}^{2}\right ) \left (\int _{\textit {\_b}}^{t}\frac {\textit {\_a}^{\frac {17}{3}} \textit {\_f}^{\frac {1}{3}}-2 \textit {\_a}^{\frac {13}{3}} \textit {\_f}^{\frac {5}{3}}-2 \textit {\_a}^{\frac {5}{3}} \textit {\_f}^{\frac {13}{3}}+\textit {\_a}^{\frac {1}{3}} \textit {\_f}^{\frac {17}{3}}+3 \textit {\_a}^{3} \textit {\_f}^{3}}{\left (\textit {\_a}^{4}+\textit {\_f}^{4}\right )^{2}}d \textit {\_a} \right )+3 t^{\frac {2}{3}} \textit {\_f}^{\frac {1}{3}}+3 \textit {\_f}}{\textit {\_f}^{\frac {4}{3}} t^{\frac {2}{3}}+\textit {\_f}^{\frac {2}{3}} t^{\frac {4}{3}}+t^{2}+\textit {\_f}^{2}}d \textit {\_f} \right )}{3}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.792 (sec). Leaf size: 53
DSolve[(t^(1/3)*y[t]^(2/3)+t)+(t^(2/3)*y[t]^(1/3)+y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \left (-t^{2/3}\right )^{3/2} \\ y(t)\to \left (-t^{4/3}+\frac {4 c_1}{3}\right ){}^{3/4} \\ y(t)\to \left (-t^{2/3}\right )^{3/2} \\ \end{align*}