82.18.21 problem Ex. 23

Internal problem ID [18843]
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. Examples on chapter III. page 38
Problem number : Ex. 23
Date solved : Tuesday, January 28, 2025 at 12:26:44 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`], _dAlembert]

\begin{align*} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 44

dsolve(exp(3*x)*(diff(y(x),x)-1)+diff(y(x),x)^3*exp(2*y(x))=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \ln \left (2\right )-\frac {3 \ln \left (3\right )}{2}+\frac {i \pi }{2}+\frac {3 x}{2} \\ y \left (x \right ) &= \frac {\ln \left (-\left ({\mathrm e}^{-x} c_{1} -1\right )^{2} {\mathrm e}^{-x} c_{1} \right )}{2}+\frac {3 x}{2} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[Exp[3*x]*(D[y[x],x]-1)+D[y[x],x]^3*Exp[2*y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out