69.1.47 problem 66

Internal problem ID [14200]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 66
Date solved : Tuesday, January 28, 2025 at 06:21:38 AM
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 &= \frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +x^{2}+1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +x^{2}+1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.407 (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*}