Internal problem ID [13961]
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: 34.7 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }-3 y^{\prime } x +\sin \left (x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=4; dsolve(x*diff(y(x),x$2)-3*x*diff(y(x),x)+sin(x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{2} x^{2}-\frac {1}{2} x^{3}\right ) y \left (0\right )+\left (x +\frac {3}{2} x^{2}+\frac {4}{3} x^{3}\right ) D\left (y \right )\left (0\right )+O\left (x^{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[x*y''[x]-3*x*y'[x]+Sin[x]*y[x]==0,y[x],{x,0,3}]
\[ y(x)\to c_1 \left (-\frac {x^3}{2}-\frac {x^2}{2}+1\right )+c_2 \left (\frac {4 x^3}{3}+\frac {3 x^2}{2}+x\right ) \]