12.10.12 problem 12

Internal problem ID [1816]
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 : 12
Date solved : Monday, January 27, 2025 at 05:35:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

\[ y = \frac {\left (c_1 \,x^{2}-4 x \sin \left (x \right )-4 \cos \left (x \right )+2 c_2 \right ) x}{2} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 25

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

\[ y(x)\to x \left (c_2 x^2-2 x \sin (x)-2 \cos (x)+c_1\right ) \]