Internal problem ID [4168]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 934.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }=4} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 49
dsolve(x^4*diff(y(x),x)^2+2*x^3*y(x)*diff(y(x),x)-4 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {2 i}{x} y \left (x \right ) = \frac {2 i}{x} y \left (x \right ) = \frac {2 \sinh \left (-\ln \left (x \right )+c_{1} \right )}{x} y \left (x \right ) = -\frac {2 \sinh \left (-\ln \left (x \right )+c_{1} \right )}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.679 (sec). Leaf size: 71
DSolve[x^4 (y'[x])^2+2 x^3 y[x] y'[x]-4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 e^{c_1}}{x^2}-\frac {e^{-c_1}}{4} y(x)\to \frac {e^{-c_1}}{4}-\frac {4 e^{c_1}}{x^2} y(x)\to -\frac {2 i}{x} y(x)\to \frac {2 i}{x} \end{align*}