40.9.7 problem 17

Internal problem ID [6717]
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
Date solved : Monday, January 27, 2025 at 02:24:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = \left ({\mathrm e}^{3 x} c_2 +{\mathrm e}^{2 x} x^{2}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+D[y[x],x]-2*y[x]==2*(1+x-x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+c_1 e^{-2 x}+c_2 e^x \]