What is a solution to the differential equation #y'=x/y=x/(1+y)#?
as currently stated, that's not a DE
By signing up, you agree to our Terms of Service and Privacy Policy
To find a solution to the differential equation ( y' = \frac{x}{y} = \frac{x}{1+y} ), we can separate variables and integrate.

Separate variables: ( \frac{dy}{dx} = \frac{x}{y} ) ( y , dy = x , dx )

Integrate both sides: ( \int y , dy = \int x , dx ) ( \frac{y^2}{2} = \frac{x^2}{2} + C )

Solve for ( y ): ( y^2 = x^2 + C ) ( y = \sqrt{x^2 + C} )

This equation represents the general solution to the given differential equation.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
 What is the volume of the solid produced by revolving #f(x)=x^32x+3, x in [0,1] #around the xaxis?
 If a particular integral of the differential equation #(D^2+2D1)y=e^(ax)# is #(4/7)e^(ax)# then the value of a is ?
 What is a solution to the differential equation #dy/dx=x^2y#?
 What is the effect of exponential growth on a population?
 How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #x=y^2#, #y=0#, and #y=sqr2# rotated about the x axis?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7