69.1.106 problem 153

Internal problem ID [14259]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 153
Date solved : Tuesday, January 28, 2025 at 06:23:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+5*y(x)=exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{7 x}+21 c_{2} {\mathrm e}^{4 x}+21 c_{1} \right ) {\mathrm e}^{-5 x}}{21} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+5*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{2 x}}{21}+c_1 e^{-5 x}+c_2 e^{-x} \]