Internal problem ID [15112]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number: 224.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_dAlembert]
\[ \boxed {y-\frac {3 x y^{\prime }}{2}-{\mathrm e}^{y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 201
dsolve(y(x)=3/2*x*diff(y(x),x)+exp(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 1 \\ \frac {27 \left (\left (-2 x^{2} \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right )^{2}-4 \left (x -\frac {2 y \left (x \right )}{3}\right ) x \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right )-4 x^{2}+\frac {8 x y \left (x \right )}{3}-\frac {8 y \left (x \right )^{2}}{9}\right ) {\mathrm e}^{\frac {-3 x \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right )+2 y \left (x \right )}{3 x}}+\operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right )^{3} x^{3}-2 y \left (x \right ) \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right )^{2} x^{2}+\frac {4 y \left (x \right )^{2} \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right ) x}{3}+\frac {c_{1} x^{2}}{27}-\frac {8 y \left (x \right )^{3}}{27}\right ) x}{{\left (3 x \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {2 y \left (x \right )}{3 x}}}{3 x}\right )-2 y \left (x \right )\right )}^{3}} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.567 (sec). Leaf size: 52
DSolve[y[x]==3/2*x*y'[x]+Exp[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=-\frac {2 e^{K[1]} \left (K[1]^2-2 K[1]+2\right )}{K[1]^3}+\frac {c_1}{K[1]^3},y(x)=\frac {3}{2} x K[1]+e^{K[1]}\right \},\{y(x),K[1]\}\right ] \]