Internal problem ID [227]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-3 y=1+x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=1+x*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-3 x} \left (\left (x^{2}-\frac {1}{2} x +8 c_{2} +\frac {1}{8}\right ) {\mathrm e}^{4 x}+8 c_{1} -\frac {8 \,{\mathrm e}^{3 x}}{3}\right )}{8} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 38
DSolve[y''[x]+2*y'[x]-3*y[x]==1+x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} e^x \left (8 x^2-4 x+1+64 c_2\right )+c_1 e^{-3 x}-\frac {1}{3} \]