Internal problem ID [12462]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.5, page 221
Problem number: 2.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = -3, y^{\prime \prime \prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([diff(y(x),x$4)-2*diff(y(x),x$3)+2*diff(y(x),x)-y(x)=0,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = -3, (D@@3)(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-x}+\left (2 x^{2}-4 x +2\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[{y''''[x]-2*y'''[x]+2*y'[x]-y[x]==0,{y[0]==1,y'[0]==-1,y''[0]==-3,y'''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (2 e^{2 x} (x-1)^2-1\right ) \]