15.22.7 problem 7

Internal problem ID [3341]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 40, page 186
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:34:33 AM
CAS classification : [[_Riccati, _special]]

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

Using series method with expansion around

\begin{align*} 2 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

Order:=6; 
dsolve([diff(y(x),x)=x^2+y(x)^2,y(2) = 0],y(x),type='series',x=2);
 

\[ y \left (x \right ) = 4 \left (x -2\right )+2 \left (x -2\right )^{2}+\frac {17}{3} \left (x -2\right )^{3}+4 \left (x -2\right )^{4}+\frac {148}{15} \left (x -2\right )^{5}+\operatorname {O}\left (\left (x -2\right )^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 41

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

\[ y(x)\to \frac {148}{15} (x-2)^5+4 (x-2)^4+\frac {17}{3} (x-2)^3+2 (x-2)^2+4 (x-2) \]