83.17.13 problem 13

Internal problem ID [19209]
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. Misc. Examples on chapter III at page 50
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 01:13:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=3\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.093 (sec). Leaf size: 46

dsolve([diff(y(x),x$2)+2*diff(y(x),x)+10*y(x)+37*sin(3*x)=0,y(1/2*Pi) = 3, D(y)(0) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-2 \sin \left (3 x \right )-6 \cos \left (3 x \right )\right ) {\mathrm e}^{\frac {\pi }{2}-x}+\left (-3 \,{\mathrm e}^{-x}+6\right ) \cos \left (3 x \right )-\sin \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 52

DSolve[{D[y[x],{x,2}]+2*D[y[x],x]+10*y[x]+37*Sin[3*x]==0,{y[Pi/2]==3,Derivative[1][y][0] == 0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (6 e^x-3-6 e^{\pi /2}\right ) \cos (3 x)-\left (e^x+2 e^{\pi /2}\right ) \sin (3 x)\right ) \]