Internal problem ID [4808]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 1179
Order:=6; dsolve(x^2*(x-5)^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(x^2-25)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {21}{50}-\frac {\sqrt {2941}}{50}} \left (1+\frac {-1166-4 \sqrt {2941}}{-3125+125 \sqrt {2941}} x -\frac {9}{15625} \frac {879 \sqrt {2941}-79709}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right )} x^{2}+\frac {\frac {15291084 \sqrt {2941}}{1953125}-\frac {906742764}{1953125}}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right ) \left (-75+\sqrt {2941}\right )} x^{3}-\frac {12}{244140625} \frac {-122814219551+2200649681 \sqrt {2941}}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right ) \left (-75+\sqrt {2941}\right ) \left (-100+\sqrt {2941}\right )} x^{4}+\frac {-\frac {10008934775328384}{152587890625}+\frac {181292058002304 \sqrt {2941}}{152587890625}}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right ) \left (-75+\sqrt {2941}\right ) \left (-100+\sqrt {2941}\right ) \left (-125+\sqrt {2941}\right )} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {21}{50}+\frac {\sqrt {2941}}{50}} \left (1+\frac {1166-4 \sqrt {2941}}{125 \sqrt {2941}+3125} x +\frac {\frac {7911 \sqrt {2941}}{15625}+\frac {717381}{15625}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right )} x^{2}+\frac {\frac {15291084 \sqrt {2941}}{1953125}+\frac {906742764}{1953125}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right ) \left (\sqrt {2941}+75\right )} x^{3}+\frac {\frac {1473770634612}{244140625}+\frac {26407796172 \sqrt {2941}}{244140625}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right ) \left (\sqrt {2941}+75\right ) \left (100+\sqrt {2941}\right )} x^{4}+\frac {\frac {10008934775328384}{152587890625}+\frac {181292058002304 \sqrt {2941}}{152587890625}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right ) \left (\sqrt {2941}+75\right ) \left (100+\sqrt {2941}\right ) \left (125+\sqrt {2941}\right )} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 5384
AsymptoticDSolveValue[x^2*(x-5)^2*y''[x]+4*x*y'[x]+(x^2-25)*y[x]==0,y[x],{x,0,5}]
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