Internal problem ID [15333]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 564.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 y^{\prime \prime }-3 y^{\prime }-2 y=5 \,{\mathrm e}^{x} \cosh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(2*diff(y(x),x$2)-3*diff(y(x),x)-2*y(x)=5*exp(x)*cosh(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {5}{4}+{\mathrm e}^{-\frac {x}{2}} c_{2} +\frac {\left (-2+5 x +10 c_{1} \right ) {\mathrm e}^{2 x}}{10} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 36
DSolve[2*y''[x]-3*y'[x]-2*y[x]==5*Exp[x]*Cosh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-x/2}+e^{2 x} \left (\frac {x}{2}-\frac {1}{5}+c_2\right )-\frac {5}{4} \]