30.1.5 problem Example, page 33

Internal problem ID [5693]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : Example, page 33
Date solved : Monday, January 27, 2025 at 01:07:23 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 7.441 (sec). Leaf size: 50

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

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