Internal problem ID [14383]
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: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{3} t -\left (t^{4}+y^{4}\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.172 (sec). Leaf size: 63
dsolve([(t*y(t)^3)-(t^4+y(t)^4)*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\frac {\sqrt {3}\, \left (6 \operatorname {RootOf}\left (\sqrt {3}\, t^{2} {\mathrm e}^{-\frac {\sqrt {3}\, \pi }{9}}-3 \tan \left (\textit {\_Z} \right ) t^{2} {\mathrm e}^{-\frac {\sqrt {3}\, \pi }{9}}-2 \sqrt {3}\, {\mathrm e}^{\frac {2 \textit {\_Z} \sqrt {3}}{3}}\right )+\pi \right )}{18}} \]
✓ Solution by Mathematica
Time used: 0.173 (sec). Leaf size: 107
DSolve[{(t*y[t]^3)-(t^4+y[t]^4)*y'[t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(t)}{t}\right )+\frac {i \left (\log \left (-\frac {2 i y(t)^2}{t^2}+\sqrt {3}+i\right )-\log \left (\frac {2 i y(t)^2}{t^2}+\sqrt {3}-i\right )\right )}{2 \sqrt {3}}=-\log (t)+\frac {i \left (\log \left (\sqrt {3}-i\right )-\log \left (\sqrt {3}+i\right )\right )}{2 \sqrt {3}},y(t)\right ] \]