74.7.22 problem 22

Internal problem ID [16099]
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 : 22
Date solved : Tuesday, January 28, 2025 at 08:40:36 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {t +4 y}{4 t +y} \end{align*}

✓ Solution by Maple

Time used: 2.186 (sec). Leaf size: 36

dsolve(diff(y(t),t)=(t+4*y(t))/(4*t+y(t)),y(t), singsol=all)
 

\[ y = \left (\operatorname {RootOf}\left (\textit {\_Z}^{10} c_{1} t^{2}-\textit {\_Z}^{6}-6 \textit {\_Z}^{4}-12 \textit {\_Z}^{2}-8\right )^{2}+1\right ) t \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 40

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

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