Internal problem ID [2307]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y y^{\prime \prime }-y^{3}-{y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 18.109 (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: 0.0 (sec). Leaf size: 0
DSolve[{y[x]*y''[x]==y[x]^3+y'[x]^2,{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
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