Internal problem ID [5374]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page
92
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=-2 x^{2}+2 x +2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=2*(1+x-x^2),y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{3 x} c_{1} +{\mathrm e}^{2 x} x^{2}+c_{2} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 23
DSolve[y''[x]+y'[x]-2*y[x]==2*(1+x-x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+c_1 e^{-2 x}+c_2 e^x \]