Internal problem ID [11653]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x +y+2 x^{6} y^{4}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 67
dsolve(x*diff(y(x),x)+y(x)=-2*x^6*y(x)^4,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\left (2 x^{3}+c_{1} \right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= -\frac {1+i \sqrt {3}}{2 \left (2 x^{3}+c_{1} \right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {i \sqrt {3}-1}{2 \left (2 x^{3}+c_{1} \right )^{\frac {1}{3}} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.87 (sec). Leaf size: 79
DSolve[x*y'[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*}