Internal problem ID [2310]
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: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {2 y y^{\prime \prime }-y^{3}-2 {y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.859 (sec). Leaf size: 15
dsolve([2*y(x)*diff(y(x),x$2)=y(x)^3+2*diff(y(x),x)^2,y(0) = -1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (2 \,\operatorname {arctanh}\left (\sqrt {\textit {\_Z} +1}\right )+x \right ) \]
✓ Solution by Mathematica
Time used: 60.205 (sec). Leaf size: 15
DSolve[{2*y[x]*y''[x]==y[x]^3+2*y'[x]^2,{y[0]==-1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\text {sech}^2\left (\frac {x}{2}\right ) \]