64.5.16 problem 16

Internal problem ID [13329]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 05:22:28 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=-2 x^{6} y^{4} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 65

dsolve(x*diff(y(x),x)+y(x)=-2*x^6*y(x)^4,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\left (2 x^{3}+c_{1} \right )^{{1}/{3}} x} \\ y &= -\frac {1+i \sqrt {3}}{2 \left (2 x^{3}+c_{1} \right )^{{1}/{3}} x} \\ y &= \frac {i \sqrt {3}-1}{2 \left (2 x^{3}+c_{1} \right )^{{1}/{3}} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.664 (sec). Leaf size: 79

DSolve[x*D[y[x],x]+y[x]==-2*x^6*y[x]^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{\sqrt [3]{x^3 \left (2 x^3+c_1\right )}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{x^3 \left (2 x^3+c_1\right )}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{x^3 \left (2 x^3+c_1\right )}} \\ y(x)\to 0 \\ \end{align*}