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...

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...

I am being asked to evaluate the first four nonzero terms using Taylor expansion about x=0. I am told the initial value problem is y'=e^y; y(0)=1 and y'(0)=-1. I am not sure how to utilize...

dP/dt=Λ-μP+μk*exp((P^2-k^2)/k^2) express equation in dimensionless form, reducing the number of parameters to one parameter (name it a). Call x the dimensionless state variable...

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...

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

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 someone help me understand what they mean when they ask for a format for the particular solution? How do I️ find?

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 general solution of the differential equation y′′+9y=13sec^2(3t), 0<t<π/6. I have gotten the characteristic equation and the roots for the first part of the general...

Find the solution of the initial value problem y′′+2y′+10y=0, y(pi/2)=0, y′(pi/2)=12. I got the answer: y(t)=4e^(pi-2t)cos(3t) Not sure where I went wrong.

Determine the values of α, if any, for which all solutions of the differential equation y′′−(2α−12)y′+(α^2−12α+27)y=0 tend to zero as t→∞; also determine the values of α, if any, for which...

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...

(1/x)(d/dx(x(dy/dx))) = 4sinh(y) : x varies from 0 to 1 Boundary Conditions :- at x = 0 : dy/dx = 0 at x = 1 : dy/dx = 4 Plot y as a function of x

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...

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

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 = ?