71.14.8 problem 14

Internal problem ID [14542]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 06:43:09 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 9.740 (sec). Leaf size: 19

dsolve([diff(y(x),x$3)-diff(y(x),x$2)+4*diff(y(x),x)-4*y(x)=0,y(0) = 0, D(y)(0) = 5, (D@@2)(y)(0) = 5],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x}-\cos \left (2 x \right )+2 \sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

DSolve[{D[y[x],{x,3}]-D[y[x],{x,2}]+4*D[y[x],x]-4*y[x]==0,{y[0]==0,Derivative[1][y][0] ==5,Derivative[2][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x+2 \sin (2 x)-\cos (2 x) \]