Internal problem ID [14891]
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: 70.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x \left (x +1\right ) y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }-10 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (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);
\[ y \left (x \right ) = \left (c_{1} +c_{2} \ln \left (x \right )\right ) \left (1+10 x +30 x^{2}+40 x^{3}+25 x^{4}+6 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (\left (-17\right ) x -\frac {157}{2} x^{2}-\frac {404}{3} x^{3}-\frac {625}{6} x^{4}-\frac {162}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]
✓ 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}]
\[ y(x)\to c_1 \left (6 x^5+25 x^4+40 x^3+30 x^2+10 x+1\right )+c_2 \left (-\frac {162 x^5}{5}-\frac {625 x^4}{6}-\frac {404 x^3}{3}-\frac {157 x^2}{2}+\left (6 x^5+25 x^4+40 x^3+30 x^2+10 x+1\right ) \log (x)-17 x\right ) \]