Internal problem ID [4799]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page
230
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
Order:=6; dsolve([(x^2+1)*diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = x -\frac {1}{3} x^{3}+\frac {1}{5} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 19
AsymptoticDSolveValue[{(x^2+1)*y''[x]+2*x*y'[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{5}-\frac {x^3}{3}+x \]