What is a solution to the differential equation #dy/dx=sqrt(xy)sinx#?
The right hand integral can be reduced to a Fresnel integral and cannot be expressed through elementary functions.
By signing up, you agree to our Terms of Service and Privacy Policy
The solution to the differential equation ( \frac{dy}{dx} = \sqrt{xy} \sin(x) ) can be found by separating variables and integrating.
-
Separate variables: [ \frac{dy}{\sqrt{y}} = \sin(x) , dx ]
-
Integrate both sides: [ \int \frac{1}{\sqrt{y}} , dy = \int \sin(x) , dx ]
[ 2\sqrt{y} = -\cos(x) + C ]
- Solve for ( y ): [ \sqrt{y} = \frac{-\cos(x)}{2} + C ]
[ y = \left(\frac{-\cos(x)}{2} + C\right)^2 ]
Where ( C ) is the constant of integration.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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.
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.
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.
- How do you evaluate the following line integral #(x^2)zds#, where c is the line segment from the point (0, 6, -1) to the point (4,1,5)?
- How do you find the general solution to #dy/dx=2yx+yx^2#?
- What is the volume of the solid produced by revolving #f(x)=xe^x-(x/2)e^x, x in [2,7] #around the x-axis?
- How do you solve #x''(t)+x3=0#?
- How do you determine if #f(x,y)=-x^3+3x^2y^2-2y^2# is homogeneous and what would it's degree be?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7