20.4.30 problem Problem 46

Internal problem ID [3665]
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
Date solved : Monday, January 27, 2025 at 07:52:58 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x)+4*x*y(x)=4*x^3*sqrt(y(x)),y(x), singsol=all)
 

\[ -x^{2}+1-c_{1} {\mathrm e}^{-x^{2}}+\sqrt {y \left (x \right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 29

DSolve[D[y[x],x]+4*x*y[x]==4*x^3*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x^2} \left (e^{x^2} \left (x^2-1\right )+c_1\right ){}^2 \]