72.7.17 problem 17

Internal problem ID [14758]
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
Date solved : Tuesday, January 28, 2025 at 07:13:59 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(t),t)=-y(t)/exp(t^2)+cos(t),y(t), singsol=all)
 

\[ y = \left (\int \cos \left (t \right ) {\mathrm e}^{\frac {\sqrt {\pi }\, \operatorname {erf}\left (t \right )}{2}}d t +c_{1} \right ) {\mathrm e}^{-\frac {\sqrt {\pi }\, \operatorname {erf}\left (t \right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 47

DSolve[D[y[t],t]==-y[t]/Exp[t^2]+Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-\frac {1}{2} \sqrt {\pi } \text {erf}(t)} \left (\int _1^te^{\frac {1}{2} \sqrt {\pi } \text {erf}(K[1])} \cos (K[1])dK[1]+c_1\right ) \]