15.18.35 problem 35

Internal problem ID [3278]
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 : 35
Date solved : Monday, January 27, 2025 at 07:30:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y y^{\prime \prime }&=y^{3}+{y^{\prime }}^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 19.756 (sec). Leaf size: 25

dsolve([y(x)*diff(y(x),x$2)=y(x)^3+diff(y(x),x)^2,y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = -\operatorname {sech}\left (\frac {\sqrt {2}\, \left (x -\sqrt {2}\, \operatorname {arctanh}\left (\sqrt {2}\right )\right )}{2}\right )^{2} \]

✗ Solution by Mathematica

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

DSolve[{y[x]*D[y[x],{x,2}]==y[x]^3+D[y[x],x]^2,{y[0]==1,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

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