Internal problem ID [2185]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+4 y x -4 x^{3} \sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 23
dsolve(diff(y(x),x)+4*x*y(x)=4*x^3*sqrt(y(x)),y(x), singsol=all)
\[ -x^{2}+1-{\mathrm e}^{-x^{2}} c_{1}+\sqrt {y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 29
DSolve[y'[x]+4*x*y[x]==4*x^3*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x^2} \left (e^{x^2} \left (x^2-1\right )+c_1\right ){}^2 \\ \end{align*}