Internal problem ID [3712]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 458.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x^{2}-y\right ) y^{\prime }-4 y x=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 53
dsolve((x^2-y(x))*diff(y(x),x) = 4*x*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {c_{1} \left (c_{1} -\sqrt {c_{1}^{2}-4 x^{2}}\right )}{2}-x^{2} y \left (x \right ) = \frac {c_{1} \left (c_{1} +\sqrt {c_{1}^{2}-4 x^{2}}\right )}{2}-x^{2} \end{align*}
✓ Solution by Mathematica
Time used: 2.966 (sec). Leaf size: 246
DSolve[(x^2-y[x])y'[x]==4 x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {i \sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}-(1-i)}\right ) y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {i \sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}}\right ) y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {\sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}}\right ) y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {\sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}-(1-i)}\right ) y(x)\to 0 y(x)\to -x^2 \end{align*}