73.24.24 problem 34.8 b(iv)

Internal problem ID [15704]
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(iv)
Date solved : Tuesday, January 28, 2025 at 08:05:38 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\sqrt {2 x^{2}+1}\, y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 47

Order:=8; 
dsolve(diff(y(x),x)+sqrt(1+2*x^2)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{2} x^{3}+\frac {3}{8} x^{4}-\frac {3}{40} x^{5}+\frac {1}{80} x^{6}-\frac {51}{560} x^{7}\right ) y \left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 53

AsymptoticDSolveValue[D[y[x],x]+Sqrt[1+2*x^2]*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (-\frac {51 x^7}{560}+\frac {x^6}{80}-\frac {3 x^5}{40}+\frac {3 x^4}{8}-\frac {x^3}{2}+\frac {x^2}{2}-x+1\right ) \]