15.18.33 problem 33

Internal problem ID [3276]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 33
Date solved : Monday, January 27, 2025 at 07:30:26 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }-y^{2} y^{\prime }&={y^{\prime }}^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.151 (sec). Leaf size: 14

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

\[ y \left (x \right ) = -\frac {6}{{\mathrm e}^{\frac {3 x}{2}}-4} \]

✓ Solution by Mathematica

Time used: 1.990 (sec). Leaf size: 18

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

\[ y(x)\to -\frac {6}{e^{3 x/2}-4} \]