Internal problem ID [5423]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page
15
Problem number: 3(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+x y-x y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 88
dsolve(diff(y(x),x)+x*y(x)=x*y(x)^4,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_{1}+1\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {1}{2 \left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_{1}+1\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_{1}+1\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {1}{2 \left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_{1}+1\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_{1}+1\right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 116
DSolve[y'[x]+x*y[x]==x*y[x]^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt [3]{1+e^{\frac {3 x^2}{2}+3 c_1}}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{1+e^{\frac {3 x^2}{2}+3 c_1}}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{1+e^{\frac {3 x^2}{2}+3 c_1}}} \\ y(x)\to 0 \\ y(x)\to 1 \\ y(x)\to -\sqrt [3]{-1} \\ y(x)\to (-1)^{2/3} \\ \end{align*}