72.7.6 problem 6

Internal problem ID [14747]
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 : 6
Date solved : Tuesday, January 28, 2025 at 07:13:34 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 19

DSolve[D[y[t],t]-2/t*y[t]==t^3*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 \left (e^t (t-1)+c_1\right ) \]