Internal problem ID [4815]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=2 \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (c_{1} x +x^{2}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 21
DSolve[y''[x]+2*y'[x]+y[x]==2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (x^2+c_2 x+c_1\right ) \]