83.43.8 problem Ex 9 page 11

Internal problem ID [19516]
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 9 page 11
Date solved : Tuesday, January 28, 2025 at 01:48:04 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {6 x -2 y-7}{2 x +3 y-6} \end{align*}

✓ Solution by Maple

Time used: 0.373 (sec). Leaf size: 33

dsolve(diff(y(x),x)=(6*x-2*y(x)-7)/(2*x+3*y(x)-6),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {3+88 \left (x -\frac {3}{2}\right )^{2} c_{1}^{2}}+\left (-4 x +12\right ) c_{1}}{6 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.130 (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*}