Internal problem ID [4880]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page
174
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 x y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+3*x*diff(y(x),x)+2*y(x)=0,y(0) = 1, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = 1+x -x^{2}-\frac {5}{6} x^{3}+\frac {2}{3} x^{4}+\frac {11}{24} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 32
AsymptoticDSolveValue[{y''[x]+3*x*y'[x]+2*y[x]==0,{y[0]==1,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {11 x^5}{24}+\frac {2 x^4}{3}-\frac {5 x^3}{6}-x^2+x+1 \]