How do you solve the differential equation #dy/dx = 7x sqrt(y)#?
Solve the differential equation.
#dy/dx = 7x sqrt(y)# for #y != 0#
Solve the differential equation.
1 Answer
Jun 28, 2017
# y= 1/16(7x^2+A)^2 #
Explanation:
We have:
# dy/dx = 7xsqrt(y) #
Which if we collect terms, (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.