74.18.64 problem 70

Internal problem ID [16621]
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
Date solved : Tuesday, January 28, 2025 at 09:12:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x \left (1+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 44

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);
 

\[ y = \left (\ln \left (x \right ) c_{2} +c_{1} \right ) \left (1+10 x +30 x^{2}+40 x^{3}+25 x^{4}+6 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (\left (-17\right ) x -\frac {157}{2} x^{2}-\frac {404}{3} x^{3}-\frac {625}{6} x^{4}-\frac {162}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 95

AsymptoticDSolveValue[x*(1+x)*D[y[x],{x,2}]+(1-2*x)*D[y[x],x]-10*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (6 x^5+25 x^4+40 x^3+30 x^2+10 x+1\right )+c_2 \left (-\frac {162 x^5}{5}-\frac {625 x^4}{6}-\frac {404 x^3}{3}-\frac {157 x^2}{2}+\left (6 x^5+25 x^4+40 x^3+30 x^2+10 x+1\right ) \log (x)-17 x\right ) \]