Internal problem ID [11709]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {4 y+\left (4 x +2 y+2\right ) y^{\prime }=-6 x -1} \] With initial conditions \begin {align*} \left [y \left (\frac {1}{2}\right ) = 3\right ] \end {align*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 23
dsolve([(6*x+4*y(x)+1)+(4*x+2*y(x)+2)*diff(y(x),x)=0,y(1/2) = 3],y(x), singsol=all)
\[ y \left (x \right ) = -2 x -1+\frac {\sqrt {4 x^{2}+12 x +93}}{2} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 28
DSolve[{(6*x+4*y[x]+1)+(4*x+2*y[x]+2)*y'[x]==0,{y[1/2]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+12 x+93}-4 x-2\right ) \]