solve the differential equation (i.e. find the equation for f(x))

Question

f'(s)=10s-12s³,f(3)=2

 

f"(x)=sinx,f'(0)=1,f(0)=6

Answer 1

Solution of differential equations-----

 

1.  f(s)= (10s^2)/2- (12s^4)/4 + c

 

     f(3)=45-12*81/4. +c = 2

 

      c=200

 

  so,  f(s)= 5s^2-3s^4+200

 

2.  f'(x)= -cos(x)+c

 

     f'(0)= -1+c=1

 

       c=2

 

     f(x)=  -sin(x)+2x +d

 

     f(0) = 6=d

 

       d=6

 

     f(x)= -sin(x)+2x+6