Internal problem ID [2390]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 41, page 195
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 879
Order:=6; dsolve(4*x^2*diff(y(x),x$2)-3*(x+x^2)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = x^{\frac {7}{8}} \left (c_{2} x^{\frac {\sqrt {17}}{8}} \left (1+\frac {21+3 \sqrt {17}}{32+8 \sqrt {17}} x +\frac {9}{128} \frac {\left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right )} x^{2}+\frac {9}{1024} \frac {\left (23+\sqrt {17}\right ) \left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right ) \left (12+\sqrt {17}\right )} x^{3}+\frac {27}{32768} \frac {\left (31+\sqrt {17}\right ) \left (23+\sqrt {17}\right ) \left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right ) \left (12+\sqrt {17}\right ) \left (16+\sqrt {17}\right )} x^{4}+\frac {81}{1310720} \frac {\left (39+\sqrt {17}\right ) \left (31+\sqrt {17}\right ) \left (23+\sqrt {17}\right ) \left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right ) \left (12+\sqrt {17}\right ) \left (16+\sqrt {17}\right ) \left (20+\sqrt {17}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} x^{-\frac {\sqrt {17}}{8}} \left (1+\frac {-21+3 \sqrt {17}}{-32+8 \sqrt {17}} x +\frac {9}{128} \frac {\left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right )} x^{2}+\frac {9}{1024} \frac {\left (-23+\sqrt {17}\right ) \left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right ) \left (-12+\sqrt {17}\right )} x^{3}+\frac {27}{32768} \frac {\left (-31+\sqrt {17}\right ) \left (-23+\sqrt {17}\right ) \left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right ) \left (-12+\sqrt {17}\right ) \left (-16+\sqrt {17}\right )} x^{4}+\frac {81}{1310720} \frac {\left (-39+\sqrt {17}\right ) \left (-31+\sqrt {17}\right ) \left (-23+\sqrt {17}\right ) \left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right ) \left (-12+\sqrt {17}\right ) \left (-16+\sqrt {17}\right ) \left (-20+\sqrt {17}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 2028
AsymptoticDSolveValue[4*x^2*y''[x]-3*(x+x^2)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
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