Internal problem ID [12702]
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: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+{\mathrm e}^{-t^{2}} y=\cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t)=-y(t)/exp(t^2)+cos(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (\int {\mathrm e}^{\frac {\sqrt {\pi }\, \operatorname {erf}\left (t \right )}{2}} \cos \left (t \right )d t +c_{1} \right ) {\mathrm e}^{-\frac {\sqrt {\pi }\, \operatorname {erf}\left (t \right )}{2}} \]
✓ Solution by Mathematica
Time used: 1.093 (sec). Leaf size: 47
DSolve[y'[t]==-y[t]/Exp[t^2]+Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-\frac {1}{2} \sqrt {\pi } \text {erf}(t)} \left (\int _1^te^{\frac {1}{2} \sqrt {\pi } \text {erf}(K[1])} \cos (K[1])dK[1]+c_1\right ) \]