Internal problem ID [1934]
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: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-3 y+\left (2 x -y+5\right ) y^{\prime }=-6 x -6} \] With initial conditions \begin {align*} [y \left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 20
dsolve([3*(2*x-y(x)+2)+(2*x-y(x)+5)*diff(y(x),x)=0,y(-1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {16}{5}-\frac {9 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {25 x}{9}+\frac {26}{9}}}{9}\right )}{5}+2 x \]
✓ Solution by Mathematica
Time used: 3.718 (sec). Leaf size: 32
DSolve[{3*(2*x-y[x]+2)+(2*x-y[x]+5)*y'[x]==0,{y[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {9}{5} W\left (\frac {1}{9} e^{\frac {25 x}{9}+\frac {26}{9}}\right )+2 x+\frac {16}{5} \]