Internal problem ID [5818]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS
ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -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: 24
Order:=8; dsolve([(x+1)*diff(y(x),x$2)-(2-x)*diff(y(x),x)+y(x)=0,y(0) = 2, D(y)(0) = -1],y(x),type='series',x=0);
\[ y \relax (x ) = 2-x -2 x^{2}-\frac {1}{3} x^{3}+\frac {1}{2} x^{4}-\frac {1}{30} x^{5}-\frac {13}{180} x^{6}+\frac {1}{28} x^{7}+\mathrm {O}\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 48
AsymptoticDSolveValue[{(x+1)*y''[x]-(2-x)*y'[x]+y[x]==0,{y[0]==2,y'[0]==-1}},y[x],{x,0,7}]
\[ y(x)\to \frac {x^7}{28}-\frac {13 x^6}{180}-\frac {x^5}{30}+\frac {x^4}{2}-\frac {x^3}{3}-2 x^2-x+2 \]