Internal problem ID [2151]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {-2 y^{\prime \prime }+3 y=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-3*diff(y(x),x$2)+3*y(x)=x*exp(x),y(x), singsol=all)
\[ y = {\mathrm e}^{\frac {\sqrt {6}\, x}{2}} c_{2} +{\mathrm e}^{-\frac {\sqrt {6}\, x}{2}} c_{1} +\left (x +4\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 54
DSolve[y''[x]-3*y'[x]+3*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (x+c_2 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+1\right ) \]