Internal problem ID [912]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+4 y x -\frac {2}{x^{2}+1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([(1+x^2)*diff(y(x),x)+4*x*y(x)=2/(1+x^2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1+2 x}{\left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 18
DSolve[{(1+x^2)*y'[x]+4*x*y[x]==2/(1+x^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x+1}{\left (x^2+1\right )^2} \\ \end{align*}