72.7.11 problem 11

Internal problem ID [14752]
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 : 11
Date solved : Tuesday, January 28, 2025 at 07:13:45 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (-2\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 15

dsolve([diff(y(t),t)-2*y(t)/t=2*t^2,y(-2) = 4],y(t), singsol=all)
 

\[ y = 2 t^{3}+5 t^{2} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 14

DSolve[{D[y[t],t]-2*y[t]/t==2*t^2,{y[-2]==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 (2 t+5) \]