Internal problem ID [11808]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve([diff(y(x),x$2)-diff(y(x),x)-6*y(x)=8*exp(2*x)-5*exp(3*x),y(0) = 3, D(y)(0) = 5],y(x), singsol=all)
\[ y \left (x \right ) = -\left (\left (-4+x \right ) {\mathrm e}^{5 x}+2 \,{\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 28
DSolve[{y''[x]-y'[x]-6*y[x]==8*Exp[2*x]-5*Exp[3*x],{y[0]==3,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{3 x} (x-4)+e^{-2 x}-2 e^{2 x} \]