Internal problem ID [12698]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\sin \left (t \right ) y=4} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(t),t)=sin(t)*y(t)+4,y(t), singsol=all)
\[ y \left (t \right ) = \left (\int 4 \,{\mathrm e}^{\cos \left (t \right )}d t +c_{1} \right ) {\mathrm e}^{-\cos \left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 29
DSolve[y'[t]==Sin[t]*y[t]+4,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-\cos (t)} \left (\int _1^t4 e^{\cos (K[1])}dK[1]+c_1\right ) \]