40.7.3 problem 12

Internal problem ID [6693]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:24:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(5*x),y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{4 x}+12 \,{\mathrm e}^{x} c_1 +12 c_2 \right ) {\mathrm e}^{x}}{12} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{5 x}}{12}+c_1 e^x+c_2 e^{2 x} \]