Internal problem ID [14089]
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: 52.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(y(x),x$3)-4*diff(y(x),x)=0,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 1-\frac {{\mathrm e}^{2 x}}{4}+\frac {{\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 23
DSolve[{y'''[x]-4*y'[x]==0,{y[0]==1,y'[0]==-1,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (e^{-2 x}-e^{2 x}+4\right ) \]