Internal problem ID [14889]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 68.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 33
Order:=6; dsolve(x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+(7-2*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{7} \left (1+\frac {1}{8} x^{2}+\frac {1}{160} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x \left (-86400+21600 x^{2}-5400 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 44
AsymptoticDSolveValue[x^2*y''[x]-7*x*y'[x]+(7-2*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{16}-\frac {x^3}{4}+x\right )+c_2 \left (\frac {x^{11}}{160}+\frac {x^9}{8}+x^7\right ) \]