Internal problem ID [14792]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(2*x^2-1)*diff(y(x),x$2)+2*x*diff(y(x),x)-3*y(x)=0,y(0) = -2, D(y)(0) = 2],y(x),type='series',x=0);
\[ y \left (x \right ) = -2+2 x +3 x^{2}-\frac {1}{3} x^{3}+\frac {5}{4} x^{4}-\frac {1}{4} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{(2*x^2-1)*y''[x]+2*x*y'[x]-3*y[x]==0,{y[0]==-2,y'[0]==2}},y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{4}+\frac {5 x^4}{4}-\frac {x^3}{3}+3 x^2+2 x-2 \]