Internal problem ID [5840]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (1+x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 55
Order:=8; dsolve((x^3-2*x^2+3*x)^2*diff(y(x),x$2)+x*(x-3)^2*diff(y(x),x)-(x+1)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {2}{3}} \left (1+\frac {1}{45} x +\frac {149}{3240} x^{2}+\frac {2701}{192456} x^{3}+\frac {236933}{121247280} x^{4}-\frac {67092967}{92754169200} x^{5}-\frac {30839263691}{50087251368000} x^{6}-\frac {14846109458423}{72576427232232000} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{1} \left (1+\frac {13}{9} x -\frac {5}{162} x^{2}+\frac {1591}{30618} x^{3}+\frac {106583}{5511240} x^{4}+\frac {7435523}{3224075400} x^{5}-\frac {70024699}{43525017900} x^{6}-\frac {2917066898}{2604972321315} x^{7}+\mathrm {O}\left (x^{8}\right )\right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 118
AsymptoticDSolveValue[(x^3-2*x^2+3*x)^2*y''[x]+x*(x-3)^2*y'[x]-(x+1)*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (-\frac {14846109458423 x^7}{72576427232232000}-\frac {30839263691 x^6}{50087251368000}-\frac {67092967 x^5}{92754169200}+\frac {236933 x^4}{121247280}+\frac {2701 x^3}{192456}+\frac {149 x^2}{3240}+\frac {x}{45}+1\right )+\frac {c_2 \left (-\frac {2917066898 x^7}{2604972321315}-\frac {70024699 x^6}{43525017900}+\frac {7435523 x^5}{3224075400}+\frac {106583 x^4}{5511240}+\frac {1591 x^3}{30618}-\frac {5 x^2}{162}+\frac {13 x}{9}+1\right )}{\sqrt [3]{x}} \]