72.7.13 problem 13

Internal problem ID [14754]
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 : 13
Date solved : Tuesday, January 28, 2025 at 07:13:51 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\sin \left (t \right ) y+4 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(t),t)=sin(t)*y(t)+4,y(t), singsol=all)
 

\[ y = \left (4 \left (\int {\mathrm e}^{\cos \left (t \right )}d t \right )+c_{1} \right ) {\mathrm e}^{-\cos \left (t \right )} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 45

DSolve[D[y[t],t]==Sin[t]*y[t]+4,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \exp \left (\int _1^t\sin (K[1])dK[1]\right ) \left (\int _1^t4 \exp \left (-\int _1^{K[2]}\sin (K[1])dK[1]\right )dK[2]+c_1\right ) \]