Internal problem ID [2305]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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: 1.908 (sec). Leaf size: 18
DSolve[{y[x]*y''[x]-y[x]^2*y'[x]==y'[x]^2,{y[0]==2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {6}{e^{3 x/2}-4} \]