10.2.34 problem 35

Internal problem ID [1162]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 35
Date solved : Monday, January 27, 2025 at 04:37:34 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +3 y}{x -y} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 21

dsolve(diff(y(x),x) = (x+3*y(x))/(x-y(x)),y(x), singsol=all)
 

\[ y = -\frac {x \left (\operatorname {LambertW}\left (-2 c_1 x \right )+2\right )}{\operatorname {LambertW}\left (-2 c_1 x \right )} \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 33

DSolve[D[y[x],x] == (x+3*y[x])/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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