77.1.38 problem 55 (page 96)

Internal problem ID [17928]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 55 (page 96)
Date solved : Tuesday, January 28, 2025 at 11:13:36 AM
CAS classification : [_exact, _rational]

\begin{align*} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.372 (sec). Leaf size: 38

dsolve((1/x-y(x)^2/(x-y(x))^2 ) +( x^2/(x-y(x))^2 - 1/y(x) ) *diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}-\ln \left (x \right ) x -c_{1} x +x \textit {\_Z} \right )} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 30

DSolve[(1/y[x]*Sin[x/y[x]]-y[x]/x^2*Cos[y[x]/x]+1 )+( 1/x*Cos[y[x]/x]-x/y[x]^2*Sin[x/y[x]]+1/y[x]^2 ) *D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{y(x)}-\sin \left (\frac {y(x)}{x}\right )+\cos \left (\frac {x}{y(x)}\right )-x=c_1,y(x)\right ] \]