74.7.17 problem 17

Internal problem ID [16094]
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 : 17
Date solved : Tuesday, January 28, 2025 at 08:39:38 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} 2 t +\left (y-3 t \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 47

dsolve(( 2*t )+( y(t)-3*t )*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \frac {2 c_{1} t -\sqrt {-4 c_{1} t +1}+1}{2 c_{1}} \\ y &= \frac {2 c_{1} t +1+\sqrt {-4 c_{1} t +1}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 40

DSolve[( 2*t  )+( y[t]-3*t )*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]-3}{(K[1]-2) (K[1]-1)}dK[1]=-\log (t)+c_1,y(t)\right ] \]