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Question 10: (1 point) We want to solve the differential equation dy/dx=[x(e^(7x+y^5)]/y4 a) This differential equation is separable...

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Advance Math


Question 10: (1 point)

We want to solve the differential equation

dy/dx=[x(e^(7x+y^5)]/y4

a) This differential equation is separable andcan be writen.

?N(y)dy=?M(x)dx ,

where

M(x)= __________

and

N(y)= __________

b) To compute the integral ?N(y)dy, you need touse the substitution

u= __________

With this substitution, we get ?N(y)dy=?n(u)du, where

n(u)= __________

We find that

?n(u)du=   __________  +K

and hence

?N(y)dy=   __________  +K,

where we have added the constant of integration K for you; soyou don't need to add one in your answer.

c) To compute the integral ?M(x)dx, you need touse integration by parts with

f(x)= __________

and

g?(x)= __________

With this choice, we get

?M(x)dx=P(x)??Q(x)dx ,

where

P(x)= __________

and

Q(x)= __________

We then find that

?M(x)dx=   __________  +D

where we have added the constant of integration D for you; soyou don't need to add one in your answer.

d)Solve ?N(y)dy=?M(x)dx for y to find thegeneral solution of the given differential equation. Then, give theparticular solution satisfying the initial condition y(0)=0.

y(x)=  __________

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