75.12.37 problem 311

Internal problem ID [16903]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 311
Date solved : Tuesday, January 28, 2025 at 09:40:25 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: 0.181 (sec). Leaf size: 142

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {2 (x-3)}{x^2-6 x+K[2]^2+4 K[2]+13}-\int _1^x\left (\frac {2 (K[2]+2) (2 K[2]+4)}{\left (K[1]^2-6 K[1]+K[2]^2+4 K[2]+13\right )^2}-\frac {2}{K[1]^2-6 K[1]+K[2]^2+4 K[2]+13}\right )dK[1]+\frac {1}{K[2]+2}\right )dK[2]+\int _1^x-\frac {2 (y(x)+2)}{K[1]^2-6 K[1]+y(x)^2+4 y(x)+13}dK[1]=c_1,y(x)\right ] \]