82.15.1 problem Ex. 1

Internal problem ID [18811]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 35
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:21:18 PM
CAS classification : [_quadrature]

\begin{align*} y&=2 y^{\prime }+3 {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 106

dsolve(y(x)=2*diff(y(x),x)+3*diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\operatorname {LambertW}\left (-\sqrt {3}\, {\mathrm e}^{-1+\frac {x}{2}-\frac {c_{1}}{2}}\right ) \left (\operatorname {LambertW}\left (-\sqrt {3}\, {\mathrm e}^{-1+\frac {x}{2}-\frac {c_{1}}{2}}\right )+2\right )}{3} \\ y \left (x \right ) &= \frac {{\mathrm e}^{2 \operatorname {RootOf}\left (-\textit {\_Z} -x +2 \,{\mathrm e}^{\textit {\_Z}}-2+c_{1} -\ln \left (3\right )+\ln \left ({\mathrm e}^{\textit {\_Z}} \left ({\mathrm e}^{\textit {\_Z}}-2\right )^{2}\right )\right )}}{3}-\frac {2 \,{\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -x +2 \,{\mathrm e}^{\textit {\_Z}}-2+c_{1} -\ln \left (3\right )+\ln \left ({\mathrm e}^{\textit {\_Z}} \left ({\mathrm e}^{\textit {\_Z}}-2\right )^{2}\right )\right )}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 18.973 (sec). Leaf size: 86

DSolve[y[x]==2*D[y[x],x]+3*D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} W\left (-e^{\frac {1}{2} (x-2-3 c_1)}\right ) \left (2+W\left (-e^{\frac {1}{2} (x-2-3 c_1)}\right )\right ) \\ y(x)\to \frac {1}{3} W\left (e^{\frac {1}{2} (x-2+3 c_1)}\right ) \left (2+W\left (e^{\frac {1}{2} (x-2+3 c_1)}\right )\right ) \\ y(x)\to 0 \\ \end{align*}