Internal problem ID [12470]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=x \,{\mathrm e}^{x}-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 52
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x*exp(x)-3*x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {9}{4}+\frac {3 x^{2}}{2}+\frac {3 x}{2}+\frac {{\mathrm e}^{x} \left (9 x^{2}+36 y \left (0\right )+18 D\left (y \right )\left (0\right )-6 x -106\right )}{54}+\frac {{\mathrm e}^{-2 x} \left (36 y \left (0\right )-36 D\left (y \right )\left (0\right )-31\right )}{108} \]
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 49
DSolve[y''[x]+y'[x]-2*y[x]==x*Exp[x]-3*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3}{4} \left (2 x^2+2 x+3\right )+\frac {1}{54} e^x \left (9 x^2-6 x+2+54 c_2\right )+c_1 e^{-2 x} \]