Internal problem ID [15472]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.1 Integration of differential equation in
series. Power series. Exercises page 171
Problem number: 728.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-y^{\prime } \sin \left (x \right )=0} \] 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: 14
Order:=6; dsolve([diff(y(x),x$2)-diff(y(x),x)*sin(x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = x +\frac {1}{6} x^{3}+\frac {1}{60} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 19
AsymptoticDSolveValue[{y''[x]+Sin[x]*y'[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{30}-\frac {x^3}{6}+x \]