74.8.10 problem 10

Internal problem ID [16146]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 08:51:59 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 15.546 (sec). Leaf size: 49

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

\[ y = \frac {t \left (\operatorname {RootOf}\left (\textit {\_Z}^{49} c_{1} t^{7}-21 \textit {\_Z}^{42} c_{1} t^{7}+147 \textit {\_Z}^{35} c_{1} t^{7}-343 \textit {\_Z}^{28} c_{1} t^{7}-64\right )^{7}-3\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 44

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

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {4 K[1]-1}{(K[1]-1) (4 K[1]+3)}dK[1]=-\log (t)+c_1,y(t)\right ] \]