Internal problem ID [12909]
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 1.3 page 47
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\left (1+t \right ) y=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([diff(y(t),t)=(t+1)*y(t),y(0) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{\frac {t \left (t +2\right )}{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 19
DSolve[{y'[t]==(t+1)*y[t],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{\frac {1}{2} t (t+2)} \]