40.1.10 problem 22

Internal problem ID [6578]
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
Date solved : Monday, January 27, 2025 at 02:14:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=2 \,{\mathrm e}^{x} \left (1-x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==2*Exp[x]*(1-x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (x^2+c_2 e^x+c_1\right ) \]