The solution of diferential equation (d y/d x)=(4 x+6 y+5/3 y+2 x+4) is

Question

The solution of diferential equation (d y/d x)=(4 x+6 y+5/3 y+2 x+4) is (A) x2+y2-x y+x-y=c (B)  y-2 x+(3/8) ℓ n (24 y+16 x+23)=c (C) 4 x y+3(x2+y2)-10(x+y)=c (D) y+2 x+(3/8) ln (24 y+16 x+23)=c

Tardigrade Admin · Accepted Answer

3 y+2 x=v ∴ 3 (d y/d x)+2=(d v/d x) ((d v/d x)-2)=(2 v+5/v+4) (d v/d x)=(6 v+15/v+4)+2=(8 v+23/v+4) (8 v+32/8 v+23) d v=8 d x ∫(1+(9/8 v+23)) d v=∫(1+(9/8 v+23)) v+(9/8) ln (8 v+23)=8 x+c y-2 x+(3/8) ln (24 y+16 x+23)=k

Q. The solution of diferential equation $\frac{d y}{d x} = \frac{4 x + 6 y + 5}{3 y + 2 x + 4}$ is

$x^{2} + y^{2} - x y + x - y = c$

$y - 2 x + \frac{3}{8} ℓ n (24 y + 16 x + 23) = c$

$4 x y + 3 (x^{2} + y^{2}) - 10 (x + y) = c$

$y + 2 x + \frac{3}{8} ln (24 y + 16 x + 23) = c$

Q. The solution of diferential equation dxdy​=3y+2x+44x+6y+5​ is

x2+y2−xy+x−y=c

y−2x+83​ℓn(24y+16x+23)=c

4xy+3(x2+y2)−10(x+y)=c

y+2x+83​ln(24y+16x+23)=c

3y+2x=v∴3dxdy​+2=dxdv​ (dxdv​−2)=v+42v+5​ dxdv​=v+46v+15​+2=v+48v+23​ 8v+238v+32​dv=8dx ∫(1+8v+239​)dv=∫(1+8v+239​) v+89​ln(8v+23)=8x+c y−2x+83​ln(24y+16x+23)=k

Q. The solution of diferential equation $\frac{d y}{d x} = \frac{4 x + 6 y + 5}{3 y + 2 x + 4}$ is

$x^{2} + y^{2} - x y + x - y = c$

$y - 2 x + \frac{3}{8} ℓ n (24 y + 16 x + 23) = c$

$4 x y + 3 (x^{2} + y^{2}) - 10 (x + y) = c$

$y + 2 x + \frac{3}{8} ln (24 y + 16 x + 23) = c$