Internal problem ID [13646]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises.
page 678
Problem number: 34.8 b(ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\sqrt {x^{2}+1}\, y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
Order:=8; dsolve(diff(y(x),x)+sqrt(1+x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}+\frac {5}{24} x^{4}-\frac {1}{15} x^{5}+\frac {13}{720} x^{6}-\frac {11}{630} x^{7}\right ) y \left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 53
AsymptoticDSolveValue[y'[x]+Sqrt[1+x^2]*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {11 x^7}{630}+\frac {13 x^6}{720}-\frac {x^5}{15}+\frac {5 x^4}{24}-\frac {x^3}{3}+\frac {x^2}{2}-x+1\right ) \]