Internal problem ID [3626]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 370.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
\[ \boxed {y^{\prime } x^{4}+y^{2} x^{4}=-a^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(x^4*diff(y(x),x)+a^2+x^4*y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-a \tan \left (\frac {a \left (c_{1} x -1\right )}{x}\right )+x}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.693 (sec). Leaf size: 87
DSolve[x^4 y'[x]+a^2+x^4 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 i a^2 c_1 e^{\frac {2 i a}{x}}+2 a c_1 x e^{\frac {2 i a}{x}}+a-i x}{x^2 \left (2 a c_1 e^{\frac {2 i a}{x}}-i\right )} \\ y(x)\to \frac {x-i a}{x^2} \\ \end{align*}