83.31.1 problem 1

Internal problem ID [19393]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (E) at page 112
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:37:13 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*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 23

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

\[ y \left (x \right ) = \frac {\tanh \left (\frac {\left (c_{2} +x \right ) \sqrt {2}}{2 c_{1}}\right ) \sqrt {2}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 10.345 (sec). Leaf size: 34

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

\[ y(x)\to \sqrt {2} \sqrt {c_1} \tanh \left (\frac {\sqrt {c_1} (x+c_2)}{\sqrt {2}}\right ) \]