Find the solution of the differential equation

Question

equation: dy/dx=(x+1)/y²  that passes through the point (-2, 2).

 

a.  y=√(1/2 x²+x+4)
 
b. y=³√(3/2 x² +2)
 

c. y=³√(3/2 x²+3x+8)
 

d. y=³√(1/2 x²+x+8)
 

e. none of these
 

Answer 1

dy/dx=(x+1)/y2

 

 

applying variable separable method

 

y² dy =(x+1) dx

 

Integrating above  we will get...

 

 y³ /3 = x²/2 + x + C

 

y³  = (3/2)x² + 3x +3C    (As it passes through the point (-2, 2) put x=-2 and y=2

 

2³ = (3/2)*(-2)² +3*(-2) +C'    ;replacing 3C with another constant C'

8  = +6 -6 +C'

8 =C'

 

So y³ = (3/2)x² + 3x +C'

     y³ =(3/2)x2 + 3x + 8

     y  = 3√(3/2 x²+3x+8)  and this your ans...