Internal problem ID [13308]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }-{\mathrm e}^{-3 y^{2}+x}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 41
dsolve(y(x)*diff(y(x),x)=exp(x-3*y(x)^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {3}\, \sqrt {\ln \left (2\right )+\ln \left (3\right )+\ln \left ({\mathrm e}^{x}+c_{1} \right )}}{3} \\ y \left (x \right ) &= \frac {\sqrt {3}\, \sqrt {\ln \left (2\right )+\ln \left (3\right )+\ln \left ({\mathrm e}^{x}+c_{1} \right )}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.781 (sec). Leaf size: 48
DSolve[y[x]*y'[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*}