Internal problem ID [4803]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page
239
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }+4 y^{\prime } x^{2}+3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^3*diff(y(x),x$2)+4*x^2*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.118 (sec). Leaf size: 282
AsymptoticDSolveValue[x^3*y''[x]+4*x^2*y'[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1 e^{-\frac {2 i \sqrt {3}}{\sqrt {x}}} \left (-\frac {14315125825 i x^{9/2}}{8796093022208 \sqrt {3}}+\frac {8083075 i x^{7/2}}{4294967296 \sqrt {3}}-\frac {15015 i \sqrt {3} x^{5/2}}{8388608}+\frac {385 i \sqrt {3} x^{3/2}}{8192}+\frac {930483178625 x^5}{844424930131968}-\frac {509233725 x^4}{549755813888}+\frac {425425 x^3}{268435456}-\frac {5005 x^2}{524288}-\frac {315 x}{512}-\frac {35 i \sqrt {x}}{16 \sqrt {3}}+1\right )}{x^{5/4}}+\frac {c_2 e^{\frac {2 i \sqrt {3}}{\sqrt {x}}} \left (\frac {14315125825 i x^{9/2}}{8796093022208 \sqrt {3}}-\frac {8083075 i x^{7/2}}{4294967296 \sqrt {3}}+\frac {15015 i \sqrt {3} x^{5/2}}{8388608}-\frac {385 i \sqrt {3} x^{3/2}}{8192}+\frac {930483178625 x^5}{844424930131968}-\frac {509233725 x^4}{549755813888}+\frac {425425 x^3}{268435456}-\frac {5005 x^2}{524288}-\frac {315 x}{512}+\frac {35 i \sqrt {x}}{16 \sqrt {3}}+1\right )}{x^{5/4}} \]