72.6.14 problem 22

Internal problem ID [14739]
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 1.8 page 121
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 07:13:17 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=t^{3}+\sin \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 35

dsolve(diff(y(t),t)+y(t)=t^3+sin(3*t),y(t), singsol=all)
 

\[ y = t^{3}-3 t^{2}+6 t -6-\frac {3 \cos \left (3 t \right )}{10}+\frac {\sin \left (3 t \right )}{10}+{\mathrm e}^{-t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 36

DSolve[D[y[t],t]+y[t]==t^3+Sin[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (\int _1^te^{K[1]} \left (K[1]^3+\sin (3 K[1])\right )dK[1]+c_1\right ) \]