Internal problem ID [4216]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter VII, Solutions in series. Examples XV. page 194
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y-3 x^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 50
Order:=6; dsolve((x-x^2)*diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=3*x^2,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \left (1-\frac {2}{3} x +\frac {1}{6} x^{2}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-2+8 x -12 x^{2}+8 x^{3}-2 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{2}}+x^{3} \left (\frac {1}{5}+\frac {1}{30} x +\frac {1}{105} x^{2}+\mathrm {O}\left (x^{3}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 91
AsymptoticDSolveValue[(x-x^2)*y''[x]+3*y'[x]+2*y[x]==3*x^2,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^2}{6}-\frac {2 x}{3}+1\right )+\frac {c_2 (1-4 x)}{x^2}+\frac {(1-4 x) \left (-\frac {5 x^6}{6}-\frac {3 x^5}{10}\right )}{x^2}+\left (\frac {x^2}{6}-\frac {2 x}{3}+1\right ) \left (-5 x^6-\frac {9 x^5}{5}+\frac {x^3}{2}\right ) \]