Evaluate the integral from (1,pi/2,0) t0 (2,pi,0) of (2xsiny +x) dx +(x^2 cosy + 3sin^3(y)) dy...

Evaluate the integral from (1,pi/2,0) t0 (2,pi,0) of (2xsiny +x) dx +(x^2 cosy + 3sin^3(y)) dy giving the potential function

Expert Solution

milcah answered 2 years ago

Let Q1=y(2) Q2 =y(3) where y=y(x) solves y'+2xy=2x^3 y(0)=1 dy/dx= (2x-y)/(x+4y) y(1)=1 y'+ycotx=y^3sin^3x y(pi/2)=1 (y^2-2x)dx+2xy dy=0 ...

Let Q1=y(2) Q2 =y(3) where y=y(x) solves y'+2xy=2x^3 y(0)=1 dy/dx= (2x-y)/(x+4y) y(1)=1 y'+ycotx=y^3sin^3x y(pi/2)=1 (y^2-2x)dx+2xy dy=0 y(1)=1 2x^2y;+4xy=3sinx y(2pi)=0 y"+2y^-1 (y')^2=y'

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...

d^2y/dx^2 − dy/dx − 3/4 y = 0, y(0) = 1, dy/dx(0) = 0, Convert the...

d^2y/dx^2 − dy/dx − 3/4 y = 0, y(0) = 1, dy/dx(0) = 0, Convert the initial value problem into a set of two coupled first-order initial value problems and find the exact solution to the differential equatiion

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

Evaluate the iterated integral. π 0 7x 0 xz 13x2 sin y dy dz dx 0

Homogenous problem. Change of variable (x-y+3)dx + (x+y-1) dy = 0

1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx) (a) What is...

1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx) (a) What is the first step of your ‘new’ integral? (b) What is the final antiderivative step before evaluating? (c) What is the answer in simplified exact form? 2) indefinite integral (cos^2 2theta) / (cos^2 theta) dtheta (a) What is the first step of your ‘new’ integral? (b) What is the simplified integral before taking the antiderivative? (c) What is the answer in simplified form?

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

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x =...

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x = 1.6 with y(0) = -1 and dy/dx(0) = 0.2. Solve with Euler’s explicit method using h = 0.4. Plot the x-y curve according to your solution.

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0)...

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method using h = 0.6 (b) solving with midpoint method using h = 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).

Question