74.5.11 problem 11

Internal problem ID [15975]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 08:25:16 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(t),t)-4*t/(1+4*t^2)*y(t)=4*t,y(t), singsol=all)
 

\[ y = 4 t^{2}+1+\sqrt {4 t^{2}+1}\, c_{1} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 26

DSolve[D[y[t],t]-4*t/(1+4*t^2)*y[t]==4*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 4 t^2+c_1 \sqrt {4 t^2+1}+1 \]