75.8.2 problem 200

Internal problem ID [16818]
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 : 200
Date solved : Tuesday, January 28, 2025 at 09:33:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.105 (sec). Leaf size: 27

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

\begin{align*} y &= 0 \\ y &= c_{1} {\mathrm e}^{x +{\mathrm e}^{x}} \\ y &= c_{1} {\mathrm e}^{-{\mathrm e}^{x}+x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 36

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

\begin{align*} y(x)\to c_1 e^{x-e^x} \\ y(x)\to c_1 e^{x+e^x} \\ y(x)\to 0 \\ \end{align*}