83.17.5 problem 5

Internal problem ID [19201]
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 : 5
Date solved : Tuesday, January 28, 2025 at 01:13:10 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=8*x^2*exp(2*x)*sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = -{\mathrm e}^{2 x} \left (2 \sin \left (2 x \right ) x^{2}+4 \cos \left (2 x \right ) x -c_{1} x -3 \sin \left (2 x \right )-c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==8*x^2*Exp[2*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\left (3-2 x^2\right ) \sin (2 x)-4 x \cos (2 x)+c_2 x+c_1\right ) \]