7.7.27 problem 27

Internal problem ID [205]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 27
Date solved : Wednesday, February 05, 2025 at 03:05:59 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 56

dsolve(3*y(x)+x^3*y(x)^4+3*x*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\left (\ln \left (x \right )+c_1 \right )^{{1}/{3}} x} \\ y &= -\frac {1+i \sqrt {3}}{2 \left (\ln \left (x \right )+c_1 \right )^{{1}/{3}} x} \\ y &= \frac {i \sqrt {3}-1}{2 \left (\ln \left (x \right )+c_1 \right )^{{1}/{3}} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.618 (sec). Leaf size: 70

DSolve[3*y[x]+x^3*y[x]^4+3*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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