83.17.14 problem 14

Internal problem ID [19210]
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 : 14
Date solved : Tuesday, January 28, 2025 at 01:13:46 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=24 x \cos \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=12 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 18

dsolve([diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=24*x*cos(x),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 12],y(x), singsol=all)
 

\[ y \left (x \right ) = -x^{2} \left (x \cos \left (x \right )-3 \sin \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 19

DSolve[{D[y[x],{x,4}]+2*D[y[x],{x,2}]+y[x]==24*x*Cos[x],{y[0]==0,Derivative[1][y][0] == 0,Derivative[2][y][0] == 0,Derivative[3][y][0] == 12}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (3 \sin (x)-x \cos (x)) \]