Internal problem ID [12806]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y=0} \] 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: 5.813 (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)
\[ y \left (x \right ) = {\mathrm e}^{x}-\cos \left (2 x \right )+2 \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 21
DSolve[{y'''[x]-y''[x]+4*y'[x]-4*y[x]==0,{y[0]==0,y'[0]==5,y''[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x+2 \sin (2 x)-\cos (2 x) \]