60.1.180 problem 181

Internal problem ID [10194]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 181
Date solved : Monday, January 27, 2025 at 06:37:29 PM
CAS classification : [_rational, [_Riccati, _special]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(x^4*(diff(y(x),x)+y(x)^2) + a=0,y(x), singsol=all)
 

\[ y = \frac {-\tan \left (\frac {\sqrt {a}\, \left (c_{1} x -1\right )}{x}\right ) \sqrt {a}+x}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.407 (sec). Leaf size: 116

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

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