Internal problem ID [12700]
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: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {y}{t^{2}}=4 \cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t)=y(t)/t^2+4*cos(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (\int 4 \,{\mathrm e}^{\frac {1}{t}} \cos \left (t \right )d t +c_{1} \right ) {\mathrm e}^{-\frac {1}{t}} \]
✓ Solution by Mathematica
Time used: 3.836 (sec). Leaf size: 34
DSolve[y'[t]==y[t]/t^2+4*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-1/t} \left (\int _1^t4 e^{\frac {1}{K[1]}} \cos (K[1])dK[1]+c_1\right ) \]