Internal problem ID [14382]
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: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{3}-y^{2} y^{\prime } t=t^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 14
dsolve([(y(t)^3-t^3)-(t*y(t)^2)*diff(y(t),t)=0,y(1) = 3],y(t), singsol=all)
\[ y \left (t \right ) = \left (-3 \ln \left (t \right )+27\right )^{\frac {1}{3}} t \]
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 22
DSolve[{(y[t]^3-t^3)-(t*y[t]^2)*y'[t]==0,{y[1]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt [3]{3} t \sqrt [3]{9-\log (t)} \]