23.2.12 problem 6(a)

Internal problem ID [4129]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 6(a)
Date solved : Monday, January 27, 2025 at 08:37:03 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=1,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} {\mathrm e}^{x}+c_{1} {\mathrm e}^{3 x}+\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x+c_2 e^{3 x}+\frac {1}{3} \]