Internal problem ID [4879]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page
174
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+4 y-1=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {5}{4}}\right ] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x)+4*y(x)=1,y(0) = 5/4],y(x),type='series',x=0);
\[ y \relax (x ) = \frac {5}{4}-4 x +8 x^{2}-\frac {32}{3} x^{3}+\frac {32}{3} x^{4}-\frac {128}{15} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
AsymptoticDSolveValue[{y'[x]+4*y[x]==1,{y[0]==125/100}},y[x],{x,0,5}]
\[ y(x)\to -\frac {128 x^5}{15}+\frac {32 x^4}{3}-\frac {32 x^3}{3}+8 x^2-4 x+\frac {5}{4} \]