Internal problem ID [11148]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 11.
Equations in which M and N are linear but not homogeneous. Page 16
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (x +y+3\right ) y^{\prime }=-4 x -2} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 33
dsolve((4*x-y(x)+2)+(x+y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -2-2 \tan \left (\operatorname {RootOf}\left (\ln \left (\frac {4}{\cos \left (\textit {\_Z} \right )^{2}}\right )-\textit {\_Z} +2 \ln \left (x +1\right )+2 c_{1} \right )\right ) \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 67
DSolve[(4*x-y[x]+2)+(x+y[x]+3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {1}{2}-\frac {5 (x+1)}{2 (y(x)+x+3)}\right )+2 \log \left (\frac {4 x^2+y(x)^2+4 y(x)+8 x+8}{5 (x+1)^2}\right )+4 \log (x+1)+5 c_1=0,y(x)\right ] \]