Internal problem ID [4737]
Book: Advanced Mathemtical Methods for Scientists and Engineers, Bender and Orszag. Springer
October 29, 1999
Section: Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page
136
Problem number: 3.24 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\sin \relax (x ) y^{\prime \prime }-2 y^{\prime } \cos \relax (x )-y \sin \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.147 (sec). Leaf size: 32
Order:=6; dsolve(sin(x)*diff(y(x),x$2)-2*cos(x)*diff(y(x),x)-sin(x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{3} \left (1-\frac {1}{10} x^{2}+\frac {1}{280} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (12-6 x^{2}+\frac {1}{2} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 44
AsymptoticDSolveValue[Sin[x]*y''[x]-2*Cos[x]*y'[x]-Sin[x]*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{24}-\frac {x^2}{2}+1\right )+c_2 \left (\frac {x^7}{280}-\frac {x^5}{10}+x^3\right ) \]