Internal problem ID [13946]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises.
page 678
Problem number: 34.5 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\tan \left (x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
Order:=6; dsolve(diff(y(x),x)-tan(x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{2} x^{2}+\frac {5}{24} x^{4}\right ) y \left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 22
AsymptoticDSolveValue[y'[x]-Tan[x]*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {5 x^4}{24}+\frac {x^2}{2}+1\right ) \]