72.7.12 problem 12

Internal problem ID [14753]
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 : 12
Date solved : Tuesday, January 28, 2025 at 07:13:48 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

dsolve([diff(y(t),t)-3/t*y(t)=2*t^3*exp(2*t),y(1) = 0],y(t), singsol=all)
 

\[ y = \left ({\mathrm e}^{2 t}-{\mathrm e}^{2}\right ) t^{3} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 20

DSolve[{D[y[t],t]-3/t*y[t]==2*t^3*Exp[2*t],{y[1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \left (e^{2 t}-e^2\right ) t^3 \]