12.5.9 problem 5

Internal problem ID [1633]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:15:18 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

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

\begin{align*} y &= \frac {1}{\sqrt {c_1 \,{\mathrm e}^{-x^{2}}-x^{2}+1}} \\ y &= -\frac {1}{\sqrt {c_1 \,{\mathrm e}^{-x^{2}}-x^{2}+1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.868 (sec). Leaf size: 80

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

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