Internal problem ID [2373]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 40, page 186
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
Order:=7; dsolve([diff(y(x),x$2)-y(x)=sin(x),y(0) = 1, D(y)(0) = 2],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+2 x +\frac {1}{2} x^{2}+\frac {1}{2} x^{3}+\frac {1}{24} x^{4}+\frac {1}{60} x^{5}+\frac {1}{720} x^{6}+\operatorname {O}\left (x^{7}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 43
AsymptoticDSolveValue[{y''[x]-y[x]==Sin[x],{y[0]==1,y'[0]==2}},y[x],{x,0,6}]
\[ y(x)\to \frac {x^6}{720}+\frac {x^5}{60}+\frac {x^4}{24}+\frac {x^3}{2}+\frac {x^2}{2}+2 x+1 \]