Internal problem ID [13414]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{4}+y^{3} y^{\prime } x=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
dsolve(1+y(x)^4+x*y(x)^3*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (-x^{4}+c_{1} \right )^{\frac {1}{4}}}{x} \\ y \left (x \right ) &= -\frac {\left (-x^{4}+c_{1} \right )^{\frac {1}{4}}}{x} \\ y \left (x \right ) &= -\frac {i \left (-x^{4}+c_{1} \right )^{\frac {1}{4}}}{x} \\ y \left (x \right ) &= \frac {i \left (-x^{4}+c_{1} \right )^{\frac {1}{4}}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 218
DSolve[1+y[x]^4+x*y[x]^3*y'[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*}