Internal problem ID [14088]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }=0} \] 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: 0.015 (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)
\[ y \left (x \right ) = -\frac {3}{4}-\frac {x}{2}+\frac {3 \,{\mathrm e}^{2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 21
DSolve[{y'''[x]-2*y''[x]==0,{y[0]==0,y'[0]==1,y''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-2 x+3 e^{2 x}-3\right ) \]