72.1.16 problem 19

Internal problem ID [14616]
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 1.2. page 33
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 06:44:40 AM
CAS classification : [_separable]

\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(v(t),t)=t^2*v(t)-2-2*v(t)+t^2,v(t), singsol=all)
 

\[ v = -1+{\mathrm e}^{\frac {t \left (t^{2}-6\right )}{3}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 27

DSolve[D[ v[t],t]==t^2*v[t]-2-2*v[t]+t^2,v[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} v(t)\to -1+c_1 e^{\frac {1}{3} t \left (t^2-6\right )} \\ v(t)\to -1 \\ \end{align*}