83.44.7 problem Ex 7 page 40

Internal problem ID [19535]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 7 page 40
Date solved : Tuesday, January 28, 2025 at 01:50:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+y&=a \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+y(x)=a*cos(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-\left (-2+\sqrt {3}\right ) x} c_{1} +{\mathrm e}^{\left (2+\sqrt {3}\right ) x} c_{2} -\frac {3 a \left (\cos \left (2 x \right )+\frac {8 \sin \left (2 x \right )}{3}\right )}{73} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 53

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+y[x]==a*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{73} a (8 \sin (2 x)+3 \cos (2 x))+c_1 e^{-\left (\left (\sqrt {3}-2\right ) x\right )}+c_2 e^{\left (2+\sqrt {3}\right ) x} \]