76.5.12 problem 12

Internal problem ID [17432]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 10:09:38 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (5\right )&=8 \end{align*}

✗ Solution by Maple

dsolve([diff(y(x),x)=(x+y(x))/(x-y(x)),y(5) = 8],y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 58

DSolve[{D[y[x],x]==(x+y[x])/(x-y[x]),{y[5]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _5^{\frac {y(x)}{x}}\frac {K[1]-1}{K[1]^2+1}dK[1]=\int _5^{\frac {8}{5}}\frac {K[1]-1}{K[1]^2+1}dK[1]-\log (x)+\log (5),y(x)\right ] \]