Internal problem ID [5683]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.3. Second-Order Linear
Equations: Ordinary Points. Page 169
Problem number: 4(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-x y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 22
Order:=8; dsolve([diff(y(x),x$2)+diff(y(x),x)-x*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = x -\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{30} x^{5}+\frac {1}{90} x^{6}-\frac {1}{1680} x^{7}+\mathrm {O}\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 47
AsymptoticDSolveValue[{y''[x]+y'[x]-x*y[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,7}]
\[ y(x)\to -\frac {x^7}{1680}+\frac {x^6}{90}-\frac {x^5}{30}+\frac {x^4}{24}+\frac {x^3}{6}-\frac {x^2}{2}+x \]