35.7.4 problem 1 (d)

Internal problem ID [6186]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 1 (d)
Date solved : Monday, January 27, 2025 at 01:47:05 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+y^{\prime } y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 8

dsolve([diff(y(x),x$2)+y(x)*diff(y(x),x)=0,y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = 2 \tanh \left (x \right ) \]

✓ Solution by Mathematica

Time used: 9.903 (sec). Leaf size: 9

DSolve[{D[y[x],{x,2}]+y[x]*D[y[x],x]==0,{y[0]==0,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \tanh (x) \]