12.10.7 problem 7

Internal problem ID [1811]
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 : 7
Date solved : Monday, January 27, 2025 at 05:35:46 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=2 x^{2}+2 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

\[ y = c_2 x +\frac {2 x^{2}}{3}-2+\frac {c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

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

\[ y(x)\to \frac {2 x^2}{3}+c_2 x+\frac {c_1}{x}-2 \]