73.6.11 problem 7.5 (a)

Internal problem ID [15150]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.5 (a)
Date solved : Tuesday, January 28, 2025 at 07:38:09 AM
CAS classification : [_separable]

\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 68

dsolve(1+y(x)^4+x*y(x)^3*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ y &= -\frac {\left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ y &= -\frac {i \left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ y &= \frac {i \left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.308 (sec). Leaf size: 218

DSolve[1+y[x]^4+x*y[x]^3*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to -\frac {i \sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to \frac {i \sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to \frac {\sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to -\sqrt [4]{-1} \\ y(x)\to \sqrt [4]{-1} \\ y(x)\to -(-1)^{3/4} \\ y(x)\to (-1)^{3/4} \\ y(x)\to \frac {i x^3}{\left (-x^4\right )^{3/4}} \\ y(x)\to \frac {x^3}{\left (-x^4\right )^{3/4}} \\ y(x)\to \frac {i \sqrt [4]{-x^4}}{x} \\ y(x)\to \frac {\sqrt [4]{-x^4}}{x} \\ \end{align*}