83.13.1 problem 2

Internal problem ID [19177]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (E) at page 39
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:11:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y \left (x \right ) = \frac {8 \,{\mathrm e}^{\frac {5 x}{2}}}{9}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 28

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

\[ y(x)\to \frac {8}{9} e^{5 x/2}+e^x (c_2 x+c_1) \]