74.6.32 problem 33

Internal problem ID [16055]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 08:31:59 AM
CAS classification : [_linear]

\begin{align*} 2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 18

dsolve([(2*t*y(t)+3*t^2)+(t^2-1)*diff(y(t),t)=0,y(0) = 1],y(t), singsol=all)
 

\[ y = \frac {-t^{2}+t -1}{t -1} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 19

DSolve[{(2*t*y[t]+3*t^2)+(t^2-1)*D[y[t],t]==0,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {-t^2+t-1}{t-1} \]