Internal problem ID [4195]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter VII, Solutions in series. Examples XIV. page 177
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (-x^{2}+x \right ) y^{\prime \prime }+3 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: 36
Order:=6; dsolve((x-x^2)*diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \left (1-\frac {2}{3} x +\frac {1}{6} x^{2}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-2+8 x -12 x^{2}+8 x^{3}-2 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 40
AsymptoticDSolveValue[(x-x^2)*y''[x]+3*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (x^2+\frac {1}{x^2}-4 x-\frac {4}{x}+6\right )+c_2 \left (\frac {x^2}{6}-\frac {2 x}{3}+1\right ) \]