Internal problem ID [14240]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {4 t y}{4 t^{2}+1}=4 t} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(y(t),t)-4*t/(1+4*t^2)*y(t)=4*t,y(t), singsol=all)
\[ y \left (t \right ) = 4 t^{2}+1+\sqrt {4 t^{2}+1}\, c_{1} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 26
DSolve[y'[t]-4*t/(1+4*t^2)*y[t]==4*t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 4 t^2+c_1 \sqrt {4 t^2+1}+1 \]