74.16.9 problem 9

Internal problem ID [16515]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 09:10:03 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (2+3 x \right ) y^{\prime \prime }+3 x y^{\prime }&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 31

Order:=6; 
dsolve((2+3*x)*diff(y(x),x$2)+3*x*diff(y(x),x)=0,y(x),type='series',x=0);
 

\[ y = y \left (0\right )+\left (x -\frac {1}{4} x^{3}+\frac {3}{16} x^{4}-\frac {9}{80} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 32

AsymptoticDSolveValue[(2+3*x)*D[y[x],{x,2}]+3*x*D[y[x],x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (-\frac {9 x^5}{80}+\frac {3 x^4}{16}-\frac {x^3}{4}+x\right )+c_1 \]