72.7.3 problem 3

Internal problem ID [14744]
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 : 3
Date solved : Tuesday, January 28, 2025 at 07:13:28 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

\[ y = \frac {3 t^{4}+4 t^{3}+12 c_{1}}{12 t +12} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 28

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

\[ y(t)\to \frac {3 t^4+4 t^3+12 c_1}{12 t+12} \]