Internal problem ID [5235]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 2. Solutions of differential equations. Supplemetary problems. Page
11
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=2 \,{\mathrm e}^{x} \left (1-x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=2*exp(x)*(1-x),y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{x} c_{1} +x^{2}+c_{2} \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 21
DSolve[y''[x]-3*y'[x]+2*y[x]==2*Exp[x]*(1-x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (x^2+c_2 e^x+c_1\right ) \]