Internal problem ID [6490]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 45
Order:=6; dsolve(x^2*diff(y(x), x, x) + (2*x+3*x^2)*diff(y(x),x)-2*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x \left (1-\frac {3}{4} x +\frac {9}{20} x^{2}-\frac {9}{40} x^{3}+\frac {27}{280} x^{4}-\frac {81}{2240} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12-36 x +54 x^{2}-54 x^{3}+\frac {81}{2} x^{4}-\frac {243}{10} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 64
AsymptoticDSolveValue[x^2*y''[x]+(2*x+3*x^2)*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {27 x^2}{8}+\frac {1}{x^2}-\frac {9 x}{2}-\frac {3}{x}+\frac {9}{2}\right )+c_2 \left (\frac {27 x^5}{280}-\frac {9 x^4}{40}+\frac {9 x^3}{20}-\frac {3 x^2}{4}+x\right ) \]