Internal problem ID [4053]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.40, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x^{2}-y\right ) y^{\prime }-4 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 53
dsolve((x^2-y(x))*diff(y(x),x)-4*x*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {c_{1} \left (-c_{1}+\sqrt {-4 x^{2}+c_{1}^{2}}\right )}{2}-x^{2} \\ y \relax (x ) = \frac {c_{1} \left (c_{1}+\sqrt {-4 x^{2}+c_{1}^{2}}\right )}{2}-x^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.57 (sec). Leaf size: 206
DSolve[(x^2-y[x])*y'[x]-4*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {i \sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} x^2-i}}-(1-i)}\right ) \\ y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {i \sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} x^2-i}}}\right ) \\ y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {\sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} x^2+i}}}\right ) \\ y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {\sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} x^2+i}}-(1-i)}\right ) \\ y(x)\to 0 \\ y(x)\to -x^2 \\ \end{align*}