20.4.27 problem Problem 43

Internal problem ID [3662]
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 43
Date solved : Monday, January 27, 2025 at 07:52:46 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(2*x*(diff(y(x),x)+y(x)^3*x^2)+y(x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {x \left (x^{2}+c_{1} \right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {x \left (x^{2}+c_{1} \right )}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.303 (sec). Leaf size: 40

DSolve[2*x*(D[y[x],x]+y[x]^3*x^2)+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {x \left (x^2+c_1\right )}} \\ y(x)\to \frac {1}{\sqrt {x \left (x^2+c_1\right )}} \\ y(x)\to 0 \\ \end{align*}