Internal problem ID [2370]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }-y^{2}=x^{2}} \] With initial conditions \begin {align*} [y \left (2\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.0 (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: 0.154 (sec). Leaf size: 9983
AsymptoticDSolveValue[{y'[x]==x^2+y[x]^2,{y[2]==0}},y[x],{x,2,5}]
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