Internal problem ID [5430]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }=\frac {2}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {1}{x}+\left (c_{1} +1\right ) \arctan \left (x \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 18
DSolve[(1+x^2)*y''[x]+2*x*y'[x]==2*x^(-3),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (1+c_1) \arctan (x)+\frac {1}{x}+c_2 \]