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Solve the differential equation #y dy/dx-y^2+9x=0# ?

1 Answer

Mar 21, 2017

#y = sqrt( C_0 e^(2x)+9(x+1/2))#

Explanation:

Think that

#y(dy)/(dx) = 1/2 d/(dx) y^2# so the equation can be read as

#1/2 d/(dx) y^2-y^2+9x=0# now calling #z=y^2# we have

#1/2 (dz)/(dx)-z+9x=0#. This equation is easy to solve giving

#z = C_0 e^(2x)+9(x+1/2)# and finally

#y = sqrt z = sqrt( C_0 e^(2x)+9(x+1/2))#

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