40.13.17 problem 38

Internal problem ID [6771]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 38
Date solved : Monday, January 27, 2025 at 02:30:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

\[ y = c_1 \,x^{2}+\ln \left (x \right ) x +c_2 x -c_1 +x \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 27

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

\[ y(x)\to x (\log (x)+1)-c_1 (x-i)^2+c_2 x \]