How do you solve the differential equation #dy/dx = 7x sqrt(y)#?

Question

Solve the differential equation.

#dy/dx = 7x sqrt(y)# for #y != 0#

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Answer 1 · 2017-06-28T10:28:42

# y= 1/16(7x^2+A)^2 #

We have:

# dy/dx = 7xsqrt(y) #

Which if we collect terms, (as #y ne0#) can be written as:

# 1/sqrt(y) \ dy/dx = 7x #

Which is a First Order non-linear separable Differential Equation, so we can "separate the variables" to get:

# int \ 1/sqrt(y) \ dy = int \ 7x \ dx #

Which we can integrate to get:

# 2sqrt(y)= (7x^2)/2 + C #

And now we can form an explicit solution:

# sqrt(y)= (7x^2)/4 + C/2 #

# :. sqrt(y)= 1/4(7x^2+A) #
# :. y= 1/16(7x^2+A)^2 #

Which, is the General Solution.