Internal problem ID [12880]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {v^{\prime }-t^{2} v+2 v=t^{2}-2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(v(t),t)=t^2*v(t)-2-2*v(t)+t^2,v(t), singsol=all)
\[ v \left (t \right ) = -1+{\mathrm e}^{\frac {t \left (t^{2}-6\right )}{3}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 27
DSolve[v'[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*}