74.7.40 problem 40

Internal problem ID [16117]
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
Date solved : Tuesday, January 28, 2025 at 08:49:34 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 15.021 (sec). Leaf size: 56

dsolve([(t*y(t)^3)-(t^4+y(t)^4)*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {\sqrt {3}\, \left (6 \operatorname {RootOf}\left (-3 \tan \left (\textit {\_Z} \right ) t^{2} {\mathrm e}^{-\frac {\pi \sqrt {3}}{9}}+\sqrt {3}\, t^{2} {\mathrm e}^{-\frac {\pi \sqrt {3}}{9}}-2 \sqrt {3}\, {\mathrm e}^{\frac {2 \sqrt {3}\, \textit {\_Z}}{3}}\right )+\pi \right )}{18}} \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 45

DSolve[{(t*y[t]^3)-(t^4+y[t]^4)*D[y[t],t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]^4+1}{K[1] \left (K[1]^4-K[1]^2+1\right )}dK[1]=-\log (t),y(t)\right ] \]