Internal problem ID [2369]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}=1} \] With initial conditions \begin {align*} [y \left (1\right ) = -1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
Order:=5; dsolve([diff(y(x),x)=1+y(x)^2,y(1) = -1],y(x),type='series',x=1);
\[ y \left (x \right ) = -1+2 \left (x -1\right )-2 \left (x -1\right )^{2}+\frac {8}{3} \left (x -1\right )^{3}-\frac {10}{3} \left (x -1\right )^{4}+\operatorname {O}\left (\left (x -1\right )^{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 35
AsymptoticDSolveValue[{y'[x]==1+y[x]^2,{y[1]==-1}},y[x],{x,1,4}]
\[ y(x)\to -\frac {10}{3} (x-1)^4+\frac {8}{3} (x-1)^3-2 (x-1)^2+2 (x-1)-1 \]