74.13.23 problem 40

Internal problem ID [16389]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 09:07:25 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 9

dsolve([diff(y(t),t$3)-2*diff(y(t),t$2)=0,y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = 0],y(t), singsol=all)
 

\[ y = 2 t +1 \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 10

DSolve[{D[ y[t],{t,3}]-2*D[y[t],{t,2}]==0,{y[0]==1,Derivative[1][y][0] ==2,Derivative[2][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 t+1 \]