77.1.28 problem 44 (page 55)

Internal problem ID [17918]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 44 (page 55)
Date solved : Tuesday, January 28, 2025 at 11:12:28 AM
CAS classification : [_rational, [_Riccati, _special]]

\begin{align*} y^{\prime }&=y^{2}+\frac {1}{x^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(diff(y(x),x)=y(x)^2+1/x^4,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 79

DSolve[D[y[x],x]==y[x]^2+1/x^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 i c_1 e^{2 i/x}+x \left (i-2 c_1 e^{2 i/x}\right )-1}{x^2 \left (2 c_1 e^{2 i/x}-i\right )} \\ y(x)\to \frac {-x+i}{x^2} \\ \end{align*}