72.7.5 problem 5

Internal problem ID [14746]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 07:13:32 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y = \left (3 \arctan \left (t \right )+c_{1} \right ) \left (t^{2}+1\right ) \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 31

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

\[ y(t)\to \left (t^2+1\right ) \left (\int _1^t\frac {3}{K[1]^2+1}dK[1]+c_1\right ) \]