12.10.17 problem 17

Internal problem ID [1821]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:36:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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

\[ y = \frac {x \left (\left (x +2 c_2 \right ) \sin \left (x \right )+2 \cos \left (x \right ) c_1 \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 49

DSolve[x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+(x^2+2)*y[x]==x^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} e^{-i x} x \left (2 i x+e^{2 i x} (-2 i x+1-4 i c_2)+1+8 c_1\right ) \]