Internal problem ID [6655]
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. CHAPTER 6 IN
REVIEW. Page 271
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+x^{2} y^{\prime }+2 x y=10 x^{3}-2 x +5} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
Order:=8; dsolve(diff(y(x),x$2)+x^2*diff(y(x),x)+2*x*y(x)=5-2*x+10*x^3,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{3} x^{3}+\frac {1}{18} x^{6}\right ) y \left (0\right )+\left (x -\frac {1}{4} x^{4}+\frac {1}{28} x^{7}\right ) D\left (y \right )\left (0\right )+\frac {5 x^{2}}{2}-\frac {x^{3}}{3}+\frac {x^{6}}{18}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 63
AsymptoticDSolveValue[y''[x]+x^2*y'[x]+2*x*y[x]==5-2*x+10*x^3,y[x],{x,0,7}]
\[ y(x)\to \frac {x^6}{18}-\frac {x^3}{3}+\frac {5 x^2}{2}+c_2 \left (\frac {x^7}{28}-\frac {x^4}{4}+x\right )+c_1 \left (\frac {x^6}{18}-\frac {x^3}{3}+1\right ) \]