28.1.104 problem 127

Internal problem ID [4410]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 127
Date solved : Monday, January 27, 2025 at 09:15:06 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: 0.033 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.168 (sec). Leaf size: 27

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

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