64.7.11 problem 11

Internal problem ID [13385]
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
Date solved : Tuesday, January 28, 2025 at 05:36:28 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {1}{2}\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.668 (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)
 

\[ y = -2 x -1+\frac {\sqrt {4 x^{2}+12 x +93}}{2} \]

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 28

DSolve[{(6*x+4*y[x]+1)+(4*x+2*y[x]+2)*D[y[x],x]==0,{y[1/2]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+12 x+93}-4 x-2\right ) \]