35.7.3 problem 1 (c)

Internal problem ID [6185]
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 (c)
Date solved : Monday, January 27, 2025 at 01:47:02 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 )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)+y(x)*diff(y(x),x)=0,y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
 

\[ y = \cot \left (\frac {x}{2}+\frac {\pi }{4}\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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