83.16.4 problem 4

Internal problem ID [19193]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (H) at page 47
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:12:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=\cosh \left (x \right ) \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)-y(x)=cosh(x)*cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 50

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

\[ y(x)\to \frac {1}{10} e^{-x} \left (2 \left (e^{2 x}-1\right ) \sin (x)-\left (e^{2 x}+1\right ) \cos (x)+10 \left (c_1 e^{2 x}+c_2\right )\right ) \]