Internal problem ID [14793]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \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)+x*diff(y(x),x)=sin(x),y(0) = 1, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+\frac {1}{6} x^{3}-\frac {1}{30} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 19
AsymptoticDSolveValue[{y''[x]+2*x*y'[x]==Sin[x],{y[0]==1,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to -\frac {7 x^5}{120}+\frac {x^3}{6}+1 \]