Internal problem ID [14785]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (3 x +2\right ) y^{\prime \prime }+3 y^{\prime } x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
Order:=6; dsolve((2+3*x)*diff(y(x),x$2)+3*x*diff(y(x),x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right )+\left (x -\frac {1}{4} x^{3}+\frac {3}{16} x^{4}-\frac {9}{80} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 32
AsymptoticDSolveValue[(2+3*x)*y''[x]+3*x*y'[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {9 x^5}{80}+\frac {3 x^4}{16}-\frac {x^3}{4}+x\right )+c_1 \]