Internal problem ID [5842]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 68
Order:=8; dsolve(x*diff(y(x),x$2)+(x+3)*diff(y(x),x)+7*x^2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1-\frac {7}{15} x^{3}+\frac {7}{120} x^{4}-\frac {1}{150} x^{5}+\frac {11}{160} x^{6}-\frac {197}{15120} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) x^{2}+\ln \relax (x ) \left (2 x^{2}-\frac {14}{15} x^{5}+\frac {7}{60} x^{6}-\frac {1}{75} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) c_{2}+\left (-2+4 x -3 x^{2}+4 x^{3}-4 x^{4}+\frac {547}{225} x^{5}-\frac {5329}{3600} x^{6}+\frac {7642}{7875} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 96
AsymptoticDSolveValue[x*y''[x]+(x+3)*y'[x]+7*x^2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {11 x^6}{160}-\frac {x^5}{150}+\frac {7 x^4}{120}-\frac {7 x^3}{15}+1\right )+c_1 \left (\frac {5539 x^6-10432 x^5+14400 x^4-14400 x^3+14400 x^2-14400 x+7200}{7200 x^2}-\frac {1}{120} \left (7 x^4-56 x^3+120\right ) \log (x)\right ) \]