Internal problem ID [1980]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Bernoulli]
\[ \boxed {2 x^{2} y y^{\prime }-2 y^{2} x=-{\mathrm e}^{x} x^{4}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(2*x^2*y(x)*diff(y(x),x)+(x^4*exp(x)-2*x*y(x)^2)=0,y(x), singsol=all)
\begin{align*} y = \sqrt {-{\mathrm e}^{x}+c_{1}}\, x y = -\sqrt {-{\mathrm e}^{x}+c_{1}}\, x \end{align*}
✓ Solution by Mathematica
Time used: 7.23 (sec). Leaf size: 45
DSolve[2*x^2*y[x]*y'[x]+(x^4*Exp[x]-2*x*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2 \left (e^x-c_1\right )} y(x)\to \sqrt {-x^2 \left (e^x-c_1\right )} \end{align*}