Home > Calculus > Solving Separable Differential Equations

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

Answer 1

Christopher Agresta

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

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))#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Charles Arocha

To solve the differential equation y(dy/dx) - y^2 + 9x = 0:

Recognize it as a first-order nonlinear ordinary differential equation.
Separate variables by moving all terms involving y to one side and terms involving x to the other side.
Integrate both sides with respect to their respective variables.
Solve for y to find the general solution.
If an initial condition is given, use it to find the particular solution.

If you have any further questions or need assistance with any step, feel free to ask.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.