Internal problem ID [13139]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y y^{\prime }-y^{2} x=6 x \,{\mathrm e}^{4 x^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve(y(x)*diff(y(x),x)-x*y(x)^2=6*x*exp(4*x^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {{\mathrm e}^{x^{2}} c_{1} +2 \,{\mathrm e}^{4 x^{2}}} y \left (x \right ) = -\sqrt {{\mathrm e}^{x^{2}} c_{1} +2 \,{\mathrm e}^{4 x^{2}}} \end{align*}
✓ Solution by Mathematica
Time used: 1.953 (sec). Leaf size: 62
DSolve[y[x]*y'[x]-x*y[x]^2==6*x*Exp[4*x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {x^2}{2}} \sqrt {2 e^{3 x^2}+c_1} y(x)\to e^{\frac {x^2}{2}} \sqrt {2 e^{3 x^2}+c_1} \end{align*}