75.17.14 problem 564

Internal problem ID [17063]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 564
Date solved : Tuesday, January 28, 2025 at 09:48:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=5 \,{\mathrm e}^{x} \cosh \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = -\frac {5}{4}+{\mathrm e}^{-\frac {x}{2}} c_{1} +\frac {\left (-2+5 x +10 c_{2} \right ) {\mathrm e}^{2 x}}{10} \]

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 36

DSolve[2*D[y[x],{x,2}]-3*D[y[x],x]-2*y[x]==5*Exp[x]*Cosh[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-x/2}+e^{2 x} \left (\frac {x}{2}-\frac {1}{5}+c_2\right )-\frac {5}{4} \]