Internal problem ID [2413]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 42, page 206
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 42
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);
\[ y \left (x \right ) = c_{1} x^{4} \left (1+2 x +3 x^{2}+4 x^{3}+5 x^{4}+6 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (-144-96 x -48 x^{2}+48 x^{4}+96 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 55
AsymptoticDSolveValue[(x-x^2)*y''[x]-3*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^4}{3}+\frac {x^2}{3}+\frac {2 x}{3}+1\right )+c_2 \left (5 x^8+4 x^7+3 x^6+2 x^5+x^4\right ) \]