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 tank holding 100 gallons of water. A pure water is pumped into the tank at a rate of 2 gal/min and the well-stirred solution is then pumped out at the same rate.

a. Determine the amount of salt in the tank at any time and How much salt is present at t  50 mi

b. At what time the concentration of the salt be 0.2 lb/gal?

c. At what time the concentration of the salt be 0.01 lb/gal?

Expert Solution

Colby Messinger answered 1 year ago

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

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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

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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'

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subject:engineering mathematics solve [cos(x+y)-sin(x+y)]dx-sin(x+y)dy=0,is the ODE exact?Find an integrating factor and solve the ODE.

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