Internal problem ID [11813]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 39.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {33}{40}}, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 30
dsolve([diff(y(x),x$3)-4*diff(y(x),x$2)+diff(y(x),x)+6*y(x)=3*x*exp(x)+2*exp(x)-sin(x),y(0) = 33/40, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {7 \,{\mathrm e}^{-x}}{20}-\frac {31 \,{\mathrm e}^{2 x}}{40}+\frac {\left (3 x +5\right ) {\mathrm e}^{x}}{4}-\frac {\sin \left (x \right )}{10} \]
✓ Solution by Mathematica
Time used: 0.285 (sec). Leaf size: 38
DSolve[{y'''[x]-4*y''[x]+y'[x]+6*y[x]==3*x*Exp[x]+2*Exp[x]-Sin[x],{y[0]==33/40,y'[0]==0,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{40} \left (10 e^x (3 x+5)+14 e^{-x}-31 e^{2 x}-4 \sin (x)\right ) \]