Internal problem ID [2011]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {3 y^{\prime } y^{2}-x y^{3}={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 88
dsolve(3*y(x)^2*diff(y(x),x)-x*y(x)^3=exp(x^2/2)*cos(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (\left (\sin \left (x \right )+c_{1} \right ) {\mathrm e}^{-x^{2}}\right )^{\frac {1}{3}} {\mathrm e}^{\frac {x^{2}}{2}} \\ y \left (x \right ) &= -\frac {\left (\left (\sin \left (x \right )+c_{1} \right ) {\mathrm e}^{-x^{2}}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right ) {\mathrm e}^{\frac {x^{2}}{2}}}{2} \\ y \left (x \right ) &= \frac {\left (\left (\sin \left (x \right )+c_{1} \right ) {\mathrm e}^{-x^{2}}\right )^{\frac {1}{3}} {\mathrm e}^{\frac {x^{2}}{2}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.426 (sec). Leaf size: 81
DSolve[3*y[x]^2*y'[x]-x*y[x]^3==Exp[x^2/2]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {x^2}{6}} \sqrt [3]{\sin (x)+c_1} \\ y(x)\to -\sqrt [3]{-1} e^{\frac {x^2}{6}} \sqrt [3]{\sin (x)+c_1} \\ y(x)\to (-1)^{2/3} e^{\frac {x^2}{6}} \sqrt [3]{\sin (x)+c_1} \\ \end{align*}