83.14.5 problem 5

Internal problem ID [19184]
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 (F) at page 42
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:11:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-4*y(x)=2*sin(1/2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{2} +{\mathrm e}^{-2 x} c_{1} -\frac {8 \sin \left (\frac {x}{2}\right )}{17} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-4*y[x]==2*Sin[1/2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {8}{17} \sin \left (\frac {x}{2}\right )+c_1 e^{2 x}+c_2 e^{-2 x} \]