Internal problem ID [14890]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 69.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 59
Order:=6; dsolve(x*(1-x)*diff(y(x),x$2)+(1+2*x)*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (c_{1} +c_{2} \ln \left (x \right )\right ) \left (1-10 x +30 x^{2}-40 x^{3}+25 x^{4}-6 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (17 x -\frac {157}{2} x^{2}+\frac {404}{3} x^{3}-\frac {625}{6} x^{4}+\frac {162}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 95
AsymptoticDSolveValue[x*(1-x)*y''[x]+(1+2*x)*y'[x]+10*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-6 x^5+25 x^4-40 x^3+30 x^2-10 x+1\right )+c_2 \left (\frac {162 x^5}{5}-\frac {625 x^4}{6}+\frac {404 x^3}{3}-\frac {157 x^2}{2}+\left (-6 x^5+25 x^4-40 x^3+30 x^2-10 x+1\right ) \log (x)+17 x\right ) \]