40.9.1 problem 11

Internal problem ID [6711]
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 : 11
Date solved : Monday, January 27, 2025 at 02:24:36 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{3 x} c_1 +\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

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

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