78.17.1 problem 1 (a)

Internal problem ID [18407]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 27. Series Solutions of First Order Equations. Problems at page 208
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 11:49:33 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 y x \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

Order:=6; 
dsolve(diff(y(x),x)=2*x*y(x),y(x),type='series',x=0);
 

\[ y = \left (1+x^{2}+\frac {1}{2} x^{4}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

AsymptoticDSolveValue[D[y[x],x]==2*x*y[x],y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^4}{2}+x^2+1\right ) \]