75.23.3 problem 726

Internal problem ID [17200]
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 ODEs). Section 18.1 Integration of differential equation in series. Power series. Exercises page 171
Problem number : 726
Date solved : Tuesday, January 28, 2025 at 09:56:57 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

Order:=6; 
dsolve([diff(y(x),x)=sin(x)*y(x),y(0) = 1],y(x),type='series',x=0);
 

\[ y = 1+\frac {1}{2} x^{2}+\frac {1}{12} x^{4}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 19

AsymptoticDSolveValue[{D[y[x],x]==Sin[x]*y[x],{y[0]==1}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {x^4}{12}+\frac {x^2}{2}+1 \]