74.1.44 problem 51

Internal problem ID [15824]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 51
Date solved : Tuesday, January 28, 2025 at 08:08:18 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 )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 15

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

\[ y = -\frac {3}{4}-\frac {x}{2}+\frac {3 \,{\mathrm e}^{2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{4} \left (-2 x+3 e^{2 x}-3\right ) \]