Internal problem ID [15102]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 214.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}-{\mathrm e}^{\frac {1}{y^{\prime }}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 71
dsolve(diff(y(x),x)^2*x=exp(1/diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {4 c_{1} \operatorname {LambertW}\left (-\frac {\sqrt {x}}{2}\right )^{2}+2 x \operatorname {LambertW}\left (-\frac {\sqrt {x}}{2}\right )+x}{4 \operatorname {LambertW}\left (-\frac {\sqrt {x}}{2}\right )^{2}} \\ y \left (x \right ) &= \frac {4 c_{1} \operatorname {LambertW}\left (\frac {\sqrt {x}}{2}\right )^{2}+2 x \operatorname {LambertW}\left (\frac {\sqrt {x}}{2}\right )+x}{4 \operatorname {LambertW}\left (\frac {\sqrt {x}}{2}\right )^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 67
DSolve[y'[x]^2*x==Exp[1/y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \int _1^x\frac {1}{2 W\left (-\frac {1}{2 \sqrt {\frac {1}{K[1]}}}\right )}dK[1]+c_1 \\ y(x)\to \int _1^x\frac {1}{2 W\left (\frac {1}{2 \sqrt {\frac {1}{K[2]}}}\right )}dK[2]+c_1 \\ \end{align*}