Internal problem ID [14762]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 53 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y=\arctan \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve([(1+x^2)^2*diff(y(x),x$2)+2*x*(1+x^2)*diff(y(x),x)+4*y(x)=arctan(x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2} \arctan \left (x \right )+\arctan \left (x \right )+3 x}{4 x^{2}+4} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 24
DSolve[{(1+x^2)^2*y''[x]+2*x*(1+x^2)*y'[x]+4*y[x]==ArcTan[x],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (2 \arctan (x)+\frac {6 x}{x^2+1}\right ) \]