72.7.15 problem 15

Internal problem ID [14756]
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
Date solved : Tuesday, January 28, 2025 at 07:13:55 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(t),t)=y(t)/t^2+4*cos(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 34

DSolve[D[y[t],t]==y[t]/t^2+4*Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-1/t} \left (\int _1^t4 e^{\frac {1}{K[1]}} \cos (K[1])dK[1]+c_1\right ) \]