Internal problem ID [15470]
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: 726.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\sin \left (x \right ) y=0} \] With initial conditions \begin {align*} [y \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)=sin(x)*y(x),y(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+\frac {1}{2} x^{2}+\frac {1}{12} x^{4}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 19
AsymptoticDSolveValue[{y'[x]==Sin[x]*y[x],{y[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{12}+\frac {x^2}{2}+1 \]