Internal problem ID [13135]
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]
\[ \boxed {x y^{3} y^{\prime }-y^{4}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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 (c_{1} x^{4}+2 x^{2}\right )^{\frac {1}{4}} y \left (x \right ) = -\left (c_{1} x^{4}+2 x^{2}\right )^{\frac {1}{4}} y \left (x \right ) = -i \left (c_{1} x^{4}+2 x^{2}\right )^{\frac {1}{4}} y \left (x \right ) = i \left (c_{1} x^{4}+2 x^{2}\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*}