Internal problem ID [2375]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime } y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \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:=7; dsolve([diff(y(x),x$2)+2*y(x)*diff(y(x),x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = x -\frac {1}{3} x^{3}+\frac {2}{15} x^{5}+\operatorname {O}\left (x^{7}\right ) \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 19
AsymptoticDSolveValue[{y''[x]+2*y[x]*y'[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,6}]
\[ y(x)\to \frac {2 x^5}{15}-\frac {x^3}{3}+x \]