47.5.6 problem 6

Internal problem ID [7495]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number : 6
Date solved : Monday, January 27, 2025 at 03:02:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=x^{2}-1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(2*x*diff(y(x),x$2)+(x-2)*diff(y(x),x)-y(x)=x^2-1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 30

DSolve[2*x*D[y[x],{x,2}]+(x-2)*D[y[x],x]-y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2-4 x+c_1 e^{-x/2}+2 c_2 (x-2)+9 \]