83.43.9 problem Ex 10 page 11

Internal problem ID [19517]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 10 page 11
Date solved : Tuesday, January 28, 2025 at 01:48:08 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 23

dsolve((2*x+y(x)+1)+(4*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (2 \,{\mathrm e}^{-2+3 x -3 c_{1}}\right )}{2}-2 x +1 \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 67

DSolve[D[y[x],x]==(6*x-2*y[x]-7)/(2*x+3*y[x]-6),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-\sqrt {22 x^2-66 x+9 (4+c_1)}-2 x+6\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {22 x^2-66 x+9 (4+c_1)}-2 x+6\right ) \\ \end{align*}