Internal problem ID [14364]
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: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{3}-y^{2} y^{\prime } t=-t^{3}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 58
dsolve(( t^3+y(t)^3 )-( t*y(t)^2 )*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \left (3 \ln \left (t \right )+c_{1} \right )^{\frac {1}{3}} t \\ y \left (t \right ) &= -\frac {\left (3 \ln \left (t \right )+c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right ) t}{2} \\ y \left (t \right ) &= \frac {\left (3 \ln \left (t \right )+c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right ) t}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 63
DSolve[( t^3+y[t]^3 )-( t*y[t]^2 )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \sqrt [3]{3 \log (t)+c_1} \\ y(t)\to -\sqrt [3]{-1} t \sqrt [3]{3 \log (t)+c_1} \\ y(t)\to (-1)^{2/3} t \sqrt [3]{3 \log (t)+c_1} \\ \end{align*}