Internal problem ID [12203]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+5 y={\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+5*y(x)=exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-5 x}+\frac {{\mathrm e}^{2 x}}{21} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 31
DSolve[y''[x]+6*y'[x]+5*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{2 x}}{21}+c_1 e^{-5 x}+c_2 e^{-x} \]