Internal problem ID [13455]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {y^{3} y^{\prime } x -y^{4}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 73
dsolve(x*y(x)^3*diff(y(x),x)=y(x)^4-x^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (x^{2} \left (c_{1} x^{2}+2\right )\right )^{\frac {1}{4}} \\ y \left (x \right ) &= -\left (x^{2} \left (c_{1} x^{2}+2\right )\right )^{\frac {1}{4}} \\ y \left (x \right ) &= -i \left (x^{2} \left (c_{1} x^{2}+2\right )\right )^{\frac {1}{4}} \\ y \left (x \right ) &= i \left (x^{2} \left (c_{1} x^{2}+2\right )\right )^{\frac {1}{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 96
DSolve[x*y[x]^3*y'[x]==y[x]^4-x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt [4]{2+c_1 x^2} \\ y(x)\to -i \sqrt {x} \sqrt [4]{2+c_1 x^2} \\ y(x)\to i \sqrt {x} \sqrt [4]{2+c_1 x^2} \\ y(x)\to \sqrt {x} \sqrt [4]{2+c_1 x^2} \\ \end{align*}