Internal problem ID [12463]
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: 3.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=2 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 3, y^{\prime \prime }\left (0\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=2*exp(x),y(0) = 1, D(y)(0) = 3, (D@@2)(y)(0) = -3],y(x), singsol=all)
\[ y \left (x \right ) = \left (x -2\right ) {\mathrm e}^{x}+3 \cos \left (x \right )+4 \sin \left (x \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y'''[x]-y'''[x]+y'[x]-y[x]==2*Exp[x],{y[0]==1,y'[0]==3,y''[0]==-3}},y[x],x,IncludeSingularSolutions -> True]
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