Internal problem ID [13996]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional
Exercises. page 715
Problem number: 35.4 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 47
Order:=6; dsolve((3*x^2-3*x^3)*diff(y(x),x$2)-(4*x+5*x^2)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}} \left (1-\frac {1}{2} x -2 x^{2}-\frac {7}{2} x^{3}-5 x^{4}-\frac {13}{2} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{2} \left (1+2 x +3 x^{2}+4 x^{3}+5 x^{4}+6 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 74
AsymptoticDSolveValue[(3*x^2-3*x^3)*y''[x]-(4*x+5*x^2)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (6 x^5+5 x^4+4 x^3+3 x^2+2 x+1\right ) x^2+c_2 \left (-\frac {13 x^5}{2}-5 x^4-\frac {7 x^3}{2}-2 x^2-\frac {x}{2}+1\right ) \sqrt [3]{x} \]