Internal problem ID [13599]
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: 33.3 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-x^{3}+2\right ) y^{\prime }-3 y x^{2}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
Order:=6; dsolve((2-x^3)*diff(y(x),x)-3*x^2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {x^{3}}{2}\right ) y \left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 15
AsymptoticDSolveValue[(2-x^3)*y'[x]-3*x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{2}+1\right ) \]