75.2.12 problem 32

Internal problem ID [16689]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 09:18:06 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \end{align*}

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 24

dsolve(diff(y(x),x)=(x+y(x))/(x-y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 36

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

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