Internal problem ID [2374]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y={\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, 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: 18
Order:=7; dsolve([diff(y(x),x$2)-2*y(x)=exp(2*x),y(0) = 0, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}+\frac {1}{10} x^{5}+\frac {7}{180} x^{6}+\operatorname {O}\left (x^{7}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 39
AsymptoticDSolveValue[{y''[x]-2*y[x]==Exp[2*x],{y[0]==0,y'[0]==0}},y[x],{x,0,6}]
\[ y(x)\to \frac {7 x^6}{180}+\frac {x^5}{10}+\frac {x^4}{4}+\frac {x^3}{3}+\frac {x^2}{2} \]