Internal problem ID [1938]
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: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (x +2 y+1\right ) y^{\prime }=-3 x -2} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✗ Solution by Maple
dsolve([(3*x-y(x)+2)+(x+2*y(x)+1)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 111
DSolve[{(3*x-y[x]+2)+(x+2*y[x]+1)*y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {6} \arctan \left (\frac {\sqrt {\frac {2}{3}} (-y(x)+3 x+2)}{2 y(x)+x+1}\right )=3 \left (\frac {2}{3} \left (\sqrt {6} \arctan \left (2 \sqrt {\frac {2}{3}}\right )+3 \log \left (\frac {25}{22}\right )-6 \log (5)\right )+2 \log \left (\frac {42 x^2+28 y(x)^2+8 y(x)+60 x+22}{(7 x+5)^2}\right )+4 \log (7 x+5)\right ),y(x)\right ] \]