Internal problem ID [4810]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-3 y=24 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=24*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{6 x} c_{1} +c_{2} {\mathrm e}^{2 x}+2\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 29
DSolve[y''[x]-2*y'[x]-3*y[x]==24*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_1 e^{2 x}+c_2 e^{6 x}+2\right ) \]