Internal problem ID [5670]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1}{\sqrt {-x^{2}+1}}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
Order:=8; dsolve(diff(y(x),x)=(1-x^2)^(-1/2),y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+x +\frac {x^{3}}{6}+\frac {3 x^{5}}{40}+\frac {5 x^{7}}{112}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 28
AsymptoticDSolveValue[y'[x]==(1-x^2)^(-1/2),y[x],{x,0,7}]
\[ y(x)\to \frac {5 x^7}{112}+\frac {3 x^5}{40}+\frac {x^3}{6}+x+c_1 \]