Internal problem ID [13943]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.11 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }-y^{2}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
Order:=5; dsolve(diff(y(x),x$2)-y(x)^2=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {x^{4} y \left (0\right )^{3}}{12}+\frac {y \left (0\right )^{2} x^{2}}{2}+\left (1+\frac {D\left (y \right )\left (0\right ) x^{3}}{3}\right ) y \left (0\right )+x D\left (y \right )\left (0\right )+\frac {D\left (y \right )\left (0\right )^{2} x^{4}}{12}+O\left (x^{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 48
AsymptoticDSolveValue[y''[x]-y[x]^2==0,y[x],{x,0,4}]
\[ y(x)\to \frac {1}{12} \left (c_1{}^3+c_2{}^2\right ) x^4+\frac {1}{3} c_1 c_2 x^3+\frac {c_1{}^2 x^2}{2}+c_2 x+c_1 \]