74.7.55 problem 60

Internal problem ID [16132]
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 : 60
Date solved : Tuesday, January 28, 2025 at 08:50:34 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(y(t)=t*(diff(y(t),t)+1)+(2*diff(y(t),t)+1),y(t), singsol=all)
 

\[ y = \left (-t -2\right ) \ln \left (t +2\right )-1+\left (t +2\right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 25

DSolve[y[t]==t*(D[y[t],t]+1)+(2*D[y[t],t]+1),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t-(t+2) \log (t+2)+c_1 t+1+2 c_1 \]