74.11.33 problem 45

Internal problem ID [16283]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 09:00:22 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(t),t$2)=t^2+exp(t)+sin(t),y(t), singsol=all)
 

\[ y = \frac {t^{4}}{12}-\sin \left (t \right )+{\mathrm e}^{t}+c_{1} t +c_{2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 39

DSolve[D[y[t],{t,2}]==t^2+Exp[t]+Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\int _1^{K[2]}\left (K[1]^2+e^{K[1]}+\sin (K[1])\right )dK[1]dK[2]+c_2 t+c_1 \]