Internal problem ID [2312]
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: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-2 {y^{\prime }}^{2}-y^{2}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = \sqrt {3}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 16
dsolve([y(x)*diff(y(x),x$2)=2*diff(y(x),x)^2+y(x)^2,y(0) = 1, D(y)(0) = 3^(1/2)],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{-\sqrt {3}\, \sin \left (x \right )+\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 19
DSolve[{y[x]*y''[x]==2*y'[x]^2+y[x]^2,{y[0]==1,y'[0]==Sqrt[3]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \csc \left (\frac {1}{6} (\pi -6 x)\right ) \]