Internal problem ID [14551]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=t^{2}+{\mathrm e}^{t}+\sin \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(t),t$2)=t^2+exp(t)+sin(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{4}}{12}-\sin \left (t \right )+{\mathrm e}^{t}+c_{1} t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 26
DSolve[y''[t]==t^2+Exp[t]+Sin[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t^4}{12}+e^t-\sin (t)+c_2 t+c_1 \]