15.3.13 problem 13

Internal problem ID [2906]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 13
Date solved : Monday, January 27, 2025 at 06:28:30 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+2+\left (y-x \right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✗ Solution by Maple

dsolve([(2*x+3*y(x)+2)+(y(x)-x)*diff(y(x),x)=0,y(0) = -2],y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 78

DSolve[{(2*x+3*y[x]+2)+(y[x]-x)*D[y[x],x]==0,{y[0]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [32 \arctan \left (\frac {2 y(x)+3 x+2}{x-y(x)}\right )=8 \log \left (\frac {10 x^2+10 x y(x)+5 y(x)^2+8 y(x)+12 x+4}{(5 x+2)^2}\right )+16 \log (5 x+2)-8 (\pi +3 \log (2)),y(x)\right ] \]