Internal problem ID [2239]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 y^{\prime \prime }+3 y^{\prime }-2 y=x^{2} {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(2*diff(y(x),x$2)+3*diff(y(x),x)-2*y(x)=x^2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x} \left (3 c_{2} {\mathrm e}^{\frac {5 x}{2}}+\left (x^{2}-\frac {14}{3} x +\frac {86}{9}\right ) {\mathrm e}^{3 x}+3 c_{1} \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 41
DSolve[2*y''[x]+3*y'[x]-2*y[x]==x^2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{27} e^x \left (9 x^2-42 x+86\right )+c_1 e^{x/2}+c_2 e^{-2 x} \]