Internal problem ID [11780]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-4 y=16 x -12 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-4*y(x)=16*x-12*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{4 x}+c_{1} {\mathrm e}^{-x}+2 \,{\mathrm e}^{2 x}-4 x +3 \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 33
DSolve[y''[x]-3*y'[x]-4*y[x]==16*x-12*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -4 x+2 e^{2 x}+c_1 e^{-x}+c_2 e^{4 x}+3 \]