77.1.14 problem 28 (page 32)

Internal problem ID [17904]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 28 (page 32)
Date solved : Tuesday, January 28, 2025 at 11:11:55 AM
CAS classification : [[_homogeneous, `class C`], _rational]

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

✓ Solution by Maple

Time used: 0.108 (sec). Leaf size: 26

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

\[ y = -2+\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (x -3\right )+c_{1} \right )\right ) \left (-x +3\right ) \]

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 27

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

\[ \text {Solve}\left [2 \arctan \left (\frac {3-x}{y(x)+2}\right )+\log (y(x)+2)=c_1,y(x)\right ] \]