Internal problem ID [11809]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2 \,{\mathrm e}^{2 x} x +6 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*x*exp(2*x)+6*exp(x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left (2 x -4\right ) {\mathrm e}^{2 x}+{\mathrm e}^{x} \left (3 x^{2}+x +5\right ) \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 25
DSolve[{y''[x]-2*y'[x]+y[x]==2*x*Exp[2*x]+6*Exp[x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (3 x^2+x+2 e^x (x-2)+5\right ) \]