Internal problem ID [11788]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=6*exp(-2*x)+3*exp(x)-4*x^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\left (2 x^{2}+2 x +3\right ) {\mathrm e}^{2 x}+\left (c_{2} +x -\frac {1}{3}\right ) {\mathrm e}^{3 x}-2 x +c_{1} -\frac {2}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 54
DSolve[y''[x]+y'[x]-2*y[x]==6*Exp[-2*x]+3*Exp[x]-4*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-2 x} \left (e^{2 x} \left (6 x^2+6 x+9\right )-6 x+e^{3 x} (3 x-1+3 c_2)-2+3 c_1\right ) \]