Internal problem ID [11772]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 42.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(x),x$3)-5*diff(y(x),x$2)+9*diff(y(x),x)-5*y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x}+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[{y'''[x]-5*y''[x]+9*y'[x]-5*y[x]==0,{y[0]==0,y'[0]==1,y''[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (2 e^x \sin (x)-e^x \cos (x)+1\right ) \]