73.3.10 problem 4.3 (j)

Internal problem ID [15044]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.3 (j)
Date solved : Tuesday, January 28, 2025 at 07:28:26 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } y&={\mathrm e}^{x -3 y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 41

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

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

✓ Solution by Mathematica

Time used: 3.560 (sec). Leaf size: 48

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

\begin{align*} y(x)\to -\frac {\sqrt {\log \left (6 \left (e^x+c_1\right )\right )}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {\log \left (6 \left (e^x+c_1\right )\right )}}{\sqrt {3}} \\ \end{align*}