29.13.16 problem 370

Internal problem ID [4970]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 370
Date solved : Monday, January 27, 2025 at 10:00:18 AM
CAS classification : [_rational, [_Riccati, _special]]

\begin{align*} x^{4} y^{\prime }+a^{2}+x^{4} y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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: 0.521 (sec). Leaf size: 94

DSolve[x^4 D[y[x],x]+a^2+x^4 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 a^2 c_1 e^{\frac {2 i a}{x}}+i a \left (e^2+2 c_1 x e^{\frac {2 i a}{x}}\right )+e^2 x}{x^2 \left (e^2+2 i a c_1 e^{\frac {2 i a}{x}}\right )} \\ y(x)\to \frac {x-i a}{x^2} \\ \end{align*}