Internal problem ID [2143]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y={\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-x} \left ({\mathrm e}^{-x} \left (x +c_{1} +1\right )-c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 24
DSolve[y''[x]+3*y'[x]+2*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (-x+c_2 e^x-1+c_1\right ) \]