A tank originally contains 100 gallons of fresh water. Water containing 5 lbs. of salt per gallon is poured into the tank at a rate of r gal/min. The mixture is allowed to leave the tank at...

A tank originally contains 100 gallons of fresh water. Water containing 5 lbs. of salt per gallon is poured into the tank at a rate of r gal/min. The mixture is allowed to leave the tank at...

Find the solution for the following exact differential equations. 2xy^2 + 4 = 2(3 - x^2y)y' ; y(-1) = 8

y=x^(1/2)+cx I can't seem to get the right answer :(

Just wondering how x^-3 + e^c = c/x^2?

I have seen it written the first way in some problems and the second in others. All have had correct answers. Can someone please explain why this is? Thank!

y'=(x^2-y^2)xy, with y(1)=2

When I solve it with separation I get to a point where y^2=5/2(x^2+1)^(1/2)+C but then I get two solutions and then my equation gets messy when trying to solve for the constant C with the...

For this equation is the Taylor Series the best approach to wstimate numerically? I am also using Euler’s to compare. Trying to find y(1) given y(x) is a solution to the equation...

Can you help me understand the steps in solving this equation? Will you always use e^() in these types of equations?

I am having trouble identifying where to start to find the U subsitute.

The nonhomogeneous equation t^2y′′−2y=29t^2−1, t>0, has homogeneous solutions y1(t)=t^2, y2(t)=t−1. Find the particular solution to the nonhomogeneous equation that does not involve any terms from...

Find the fundamental set of solutions for the given differential equation L[y]=y′′−9y′+20y=0 and initial point t0=0 that also specifies y1(t0)=1, y′1(t0)=0, y2(t0)=0 and y′2(t0)=1.

Find the solution of the given initial value problem in explicit form. sin(2x)dx+cos(4y)dy=0, y(π/2)=π/4 I solve to get the general equation: (1/4)sin(4y)=(1/2)cos(2x)+C then...

A rocket sled having an initial speed of 191 mi/h is slowed by a channel of water. Assume that during the braking process, the acceleration a is given by a(v)=−μυ^2, where v is the velocity and μ...

Find the solution of the given initial value problem in explicit form. sin(2x)dx+cos(4y)dy=0, y(π/2)=π/4 I solve to get the general equation: y=[arcsin(2cos(2x)+C)]/4...

Find the solution of the differential equation dy/dx*(ln(y))^2 = yx^2 which satisfies the initial condition y(1)=e^2 y = ?

Find the particular solution of the differential equation: x^2/(y^2-4)*dy/dx = 1/(2y) satisfying the initial condition y(1)=sqrt(5) y = ? the answer must be the...

This is an assignment question.

Solve the separable differential equation for u: du/dt = e^(4u+9t) Use the following initial condition: u(0)=4 u = ?

Solve the separable differential equation 7x - 6y*sqrt(x^2+1)dy/dx = 0 Subject to the initial condition: y(0)=5 y = ?