Internal problem ID [14795]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Van_der_Pol]
\[ \boxed {y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
Order:=6; dsolve([diff(y(x),x$2)+(y(x)^2-1)*diff(y(x),x)+y(x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = x +\frac {1}{2} x^{2}-\frac {1}{8} x^{4}-\frac {1}{8} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 26
AsymptoticDSolveValue[{y''[x]+(y[x]^2-1)*y'[x]+y[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{8}-\frac {x^4}{8}+\frac {x^2}{2}+x \]