Internal problem ID [13514]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.6 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]
\[ \boxed {2 x y^{\prime } y^{\prime \prime }-{y^{\prime }}^{2}=-1} \] With initial conditions \begin {align*} \left [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = \sqrt {3}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 19
dsolve([2*x*diff(y(x),x)*diff(y(x),x$2)=diff(y(x),x)^2-1,y(1) = 0, D(y)(1) = 3^(1/2)],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 x +1\right )^{\frac {3}{2}}}{3}-\sqrt {3} \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 26
DSolve[{2*x*y'[x]*y''[x]==y'[x]^2-1,{y[1]==0,y'[1]==Sqrt[3]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left ((2 x+1)^{3/2}-3 \sqrt {3}\right ) \]