Question

In: Advanced Math

dy/dx + y/x \ x3y2

dy/dx + y/x \ x³y²

Expert Solution

Solution: The given diffrential equation is --------(1) is first order first and degree diffrential equation.

This is of the form where is known as Bernoliie's diffrential equation.

Dividing equation (1) with , we get

--------(2)

-----------(3)

put

Equation (3) becomes

that implies ------(4)

This is of the form where

which is Linear diffrential Equation in 't'.

Integrating factor(I F )=

I F = =

Therefore Integrating factor ( I F ) =

The solution of (4) is given by ------(5)

------(6)

replace t by in (6)

we get

The solution of is .

Colby Messinger answered 1 year ago

dy/dx+(y/2x)=(x/(y^3))

Solve the following DEs 1.) dy/dx + y =e^3x 2.) x^2y' +xy = 1 3,) x(dy/dx)-y...

Solve the following DEs 1.) dy/dx + y =e^3x 2.) x^2y' +xy = 1 3,) x(dy/dx)-y = x^2 sin(x) 4.) y' - 2y = e^2x, y(0) = 2 5.) cos(x)(dy/dx) + ysin(x) = 1, y(pi/4) = 0

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

Let (X, dX) and (Y, dY) be metric spaces.Define the function d : (X × Y...

Let (X, dX) and (Y, dY) be metric spaces.Define the function d : (X × Y ) × (X × Y ) → R by d ((x1, y1), (x2,y2)) = dx(x1,x2)+dy(y1,y2) Prove that d is a metric on X × Y .

Suppose (X, dX) and (Y, dY ) are metric spaces. Define d : (X ×Y )×(X...

Suppose (X, dX) and (Y, dY ) are metric spaces. Define d : (X ×Y )×(X × Y ) → R by d((x, y),(a, b)) = dX(x, a) + dY (y, b). Prove d is a metric on X × Y .

Solve these first-order Differential Equations using an integrating factor. 1. dy/dx+2xy=0 2. dy/dx-y=5 3. dy/dx+y=x 4....

Solve these first-order Differential Equations using an integrating factor. 1. dy/dx+2xy=0 2. dy/dx-y=5 3. dy/dx+y=x 4. (x)dy/dx+(x+1)y=3/x 5. (x^2)dy/dx=e^x-2xy

((sqrtx)+1)dy/dx=(ysqrtx)/(x) + sqrt(y/x), y(2)=1

Find dy/dx by implicit differentiation: cos(x+y)=y^3 sin x

Solve IVP for y(x): dy/dx + (3/x)y = 8y^4, y(1) = 1

Let (X,dX),(Y,dY ) be metric spaces and f: X → Y be a continuous bijection. Prove...

Let (X,dX),(Y,dY ) be metric spaces and f: X → Y be a continuous bijection. Prove that if (X, dX ) is compact, then f is a homeomorphism. (Hint: it might be convenient to use that a function is continuous if and only if the inverse image of every open set is open, if and only if the inverse image of every closed set is closed).