Internal problem ID [14811]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+2 y^{\prime } x +y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 60
Order:=6; dsolve(x*diff(y(x),x$2)+2*x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x \left (1-\frac {3}{2} x +\frac {5}{4} x^{2}-\frac {35}{48} x^{3}+\frac {21}{64} x^{4}-\frac {77}{640} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (-x +\frac {3}{2} x^{2}-\frac {5}{4} x^{3}+\frac {35}{48} x^{4}-\frac {21}{64} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (1-2 x +\frac {7}{4} x^{2}-\frac {11}{12} x^{3}+\frac {61}{192} x^{4}-\frac {131}{1920} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 87
AsymptoticDSolveValue[x*y''[x]+2*x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{48} x \left (35 x^3-60 x^2+72 x-48\right ) \log (x)+\frac {1}{192} \left (-79 x^4+64 x^3+48 x^2-192 x+192\right )\right )+c_2 \left (\frac {21 x^5}{64}-\frac {35 x^4}{48}+\frac {5 x^3}{4}-\frac {3 x^2}{2}+x\right ) \]