73.7.49 problem 49

Internal problem ID [15207]
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 : 49
Date solved : Tuesday, January 28, 2025 at 07:49:56 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} x \left (1-2 y\right )+\left (y-x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 45

dsolve(x*(1-2*y(x))+(y(x)-x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= x^{2}-\sqrt {x^{4}-x^{2}-2 c_{1}} \\ y &= x^{2}+\sqrt {x^{4}-x^{2}-2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 66

DSolve[x*(1-2*y[x])+(y[x]-x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2-i \sqrt {-x^4+x^2-c_1} \\ y(x)\to x^2+i \sqrt {-x^4+x^2-c_1} \\ y(x)\to \frac {1}{2} \\ \end{align*}