15.15.11 problem 12

Internal problem ID [3215]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:26:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{2} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=x^2*sin(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{3 x}+\frac {\left (25 x^{2}+55 x +28\right ) \cos \left (x \right )}{125}+\frac {\left (25 x^{2}-20 x -67\right ) \sin \left (x \right )}{250}+c_2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 52

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==x^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{250} \left (\left (25 x^2-20 x-67\right ) \sin (x)+2 \left (25 x^2+55 x+28\right ) \cos (x)\right )+c_1 e^x+c_2 e^{3 x} \]