Internal problem ID [5698]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.4. REGULAR SINGULAR
POINTS. Page 175
Problem number: 3(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 51
Order:=8; dsolve(4*x^2*diff(y(x),x$2)+(2*x^4-5*x)*diff(y(x),x)+(3*x^2+2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {1}{4}} \left (1-\frac {3}{2} x^{2}-\frac {1}{30} x^{3}+\frac {1}{8} x^{4}+\frac {137}{1300} x^{5}-\frac {19}{12240} x^{6}-\frac {7169}{764400} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} x^{2} \left (1-\frac {1}{10} x^{2}-\frac {4}{57} x^{3}+\frac {3}{920} x^{4}+\frac {32}{4275} x^{5}+\frac {36287}{9753840} x^{6}-\frac {4037}{16059750} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 106
AsymptoticDSolveValue[4*x^2*y''[x]+(2*x^4-5*x)*y'[x]+(3*x^2+2)*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {4037 x^7}{16059750}+\frac {36287 x^6}{9753840}+\frac {32 x^5}{4275}+\frac {3 x^4}{920}-\frac {4 x^3}{57}-\frac {x^2}{10}+1\right ) x^2+c_2 \left (-\frac {7169 x^7}{764400}-\frac {19 x^6}{12240}+\frac {137 x^5}{1300}+\frac {x^4}{8}-\frac {x^3}{30}-\frac {3 x^2}{2}+1\right ) \sqrt [4]{x} \]