40.14.2 problem 23

Internal problem ID [6773]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:30:12 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=\frac {2}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve((1+x^2)*diff(y(x),x$2)+2*x*diff(y(x),x)=2*x^(-3),y(x), singsol=all)
 

\[ y = \frac {1}{x}+\left (c_1 +1\right ) \arctan \left (x \right )+c_2 \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 18

DSolve[(1+x^2)*D[y[x],{x,2}]+2*x*D[y[x],x]==2*x^(-3),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (1+c_1) \arctan (x)+\frac {1}{x}+c_2 \]