Consider the differential equation
Given that y(0)=0.5, solve the differential equation by separating the variables and integrating. Given that
for some constant L, find the value of L.
Hint: You may use the fact that

Want to see the full answer?
Check out a sample Q&A here


Related Calculus Q&A
Find answers to questions asked by students like you.
Q: Use the annihilator method to find a general solution to the given differential equation.…
A: Given differential equation. y''+2y'+2y=e^-x cosx+x^2
Q: (b). Use the method of separation of variables to solve the differential equation y? dy = In x x3 dx
A: Click to see the answer
Q: Find the particular solution of the differential equation that satisfies the initial conditions.
A: The given differential equation is in variable separable form. Hence, an be solved using simple…
Q: Given that y = e^x is a solution of (x - 1)y" - (x + 1)y' + 2y = 0, find a linearly independent…
A: The solution is given as
Q: Q3/ Find the IVP for the differential equation. x²y" - 3xy² + 68y=0, that satisfies the -зху!…
A: Follow the procedure given below.
Q: Given a differential equation as d²y x2 dx² +4y=0. dx By using substitution of x = e' and t = ln…
A: Click to see the answer
Q: Consider the differential equation (xy + x)dx = (x²y² – x² + y² – 1) dy. By separation of variables,…
A: Click to see the answer
Q: Calculate the value(s) of C for which y=x'-2C is a solution to the differential equation dy -3y-54 =…
A: We have to find the value of C
Q: a. if y = asin3x + bcos3x satisfies the differential equation d?y + 4 + 3y = 10cos3x, find a, b. dx2…
A: Now , first we will find d^2y/ dx^2 and dy/dx Then, we will find the value of a and b.
Q: Find a general solution for the given differential equation with x as the independent variable.…
A: Click to see the answer
Q: Apply the undetermined coefficients method to find a particular solution of the to!lowing…
A: Click to see the answer
Q: Determine the values of r for which the differential equation y′+2y=0 has solutions of the form…
A: Click to see the answer
Q: Verify that the function y = e-3x is a solution to the differential equation d2ydx2 + dydx − 6y = 0.
A: We have to verify the solution
Q: d. 2ydx +x(x² In y – 1)dy = 0 -
A: Click to see the answer
Q: Solve the given differential equation by using an appropriate substitution: dy/dx = (x+3y) / (3x +…
A: Step-1 Solve the given differential equation by using an apprapriate substitition…
Q: Solve the differential equation (1+e2x)dy + (1+y2)dx=0 ,given that y=1 at x=0.
A: Given- 1+y2dx+1+e2xdy=0 To find- The solution of the above differential equation at 1,0. Concept…
Q: determine the value of C of the general solution of the separable differential equation dy/dx= 2y/x…
A: Given: A differential equation dydx=2yx As this is a separable differential equation so it can be…
Q: Solve the given differential equation by using separable variables. 1. dy x-5 = dx y²
A: Click to see the answer
Q: Determine the general solution of the given Differential Equation (x² – xy + y²)dx – xydy = 0 -
A: Click to see the answer
Q: dy 2 dx y+2 x+y- 1
A: Click to see the answer
Q: By using the substitution z = y², convert the differential equation dy x²y- xy2 = 1. dx to a linear…
A: Click to see the answer
Q: find the general solution of the given differential equation. 8.y″ − 2y′ + y = et/(1 + t2)
A: Click to see the answer
Q: Find the general solution of the first-order differential equation x dx + ( y…
A: Consider the following differential equation: xdx+y+eyx2+1dy=0y+eyx2+1dy=-xdxy+eydy=-xx2+1dx…
Q: Determine whether the function y = ln x + e2x + Cx4 is a solution of the differential equation y(4)…
A: Given differential equation is y(4)-16y=0 Given function is y=lnx+e2x+cx4 Differentiate y repeatedly…
Q: Solve the Euler Cauchy differential equation d²y x2. dx2 dy +y32(Inx) dx -
A: Click to see the answer
Q: Consider the differential equation Y+ 2y = 4x - 3e*, given that y(0) = 1 and y (0) = 2. What would…
A: Given, Y"+2y' =4x-3ex
Q: Solve the differential equation dy xy y(0) = -3. dx V1+ x? There is no need to isolate y.
A: Click to see the answer
Q: Find the general solution of the differential equation given below ylnxlnydx + dy = 0
A: We will solve it using separating the variables
Q: solve the first order homogenous differential equation (x² + æy) dy = (æ² + y²) dæl
A: The differential equation is given as x2+xydy = x2+y2dx It can be rewritten as dydx = x2+y2x2+xy…
Q: Given, (1/x2+1/y6)dx+(Ax+1/y7)dy=0 is an exact differential equation. Determine the value of A.
A: We have to find
Q: determine the value of C of the general solution of the separable differential equation dy/dx= xy^2…
A: From the given problem: dydx=xy2 So, dydx=xy2dy=xy2dxdyy2=xdx Now integrate on both side:…
Q: Find the particular solution to the given differential equation that satisfies the given conditions.…
A: Given differential equation is: d2ydx2-2dydx+y=e-4x(x-1); y'(0)=0, y(0)=0 Solution of…
Q: 2. Make up a differential equation of the form dy dt that has the function y(t) = e²t = 2yt+g(y) as…
A: Click to see the answer
Q: Solve the non-homogenous differential equation below dy 2y + x - 3 dx y + 2x – 3
A: Click to see the answer
Q: Find the general solution of the separable differential equation dy dxy (2x + 3) e3y
A: Click to see the answer
Q: Solve the differential equation with the given initial value condition: dy/dx = xy + 2x ; y(0) =
A: Click to see the answer
Q: Show that the differential equation dy / dx = y / x is inexact and that a factor of 1 / x ^ 2 can…
A: Given differential equation is, dydx=yx.
Q: Find the particular solution to the given differential equation that satisfies the given conditions.…
A: We have d2ydx2-2dydx+y=xe6x-e6x ; dydx=0 and y=0 when x=0 The given equation can be written as…
Q: For which value of a is the differential equation (y² + axy³ )dx + (Ky²x² + 2xy) dy = 0 exact
A: Click to see the answer
Q: Solve the given differential equation by using an appropriate substitution. (x² + y²)dx + (x² +…
A: Click to see the answer
Q: Find the particular solution to the given differential equation that satisfies the given conditions.…
A: Let y = emx is the solution to the differential equation, so…
Q: Solve the non-homogenous differential equation below dy 2y + x – 3 dx y+ 2х —3
A: Given that a non homogeneous differential equations and we solve by using general property of…
Q: Find a general solution for the given differential equation with x as the independent variable.…
A: Click to see the answer
Q: Evaluate and solve the linear differential equation. (d2x)/(dt2) + 2 (dx)/(dt) + 5x = 8e-t, when t…
A: Given differential equation can be writen as, (D2+2D+5)x=8e-t.....(i)d=ddt,…
Q: Given: 1+ ce' y 1- ce dy Determine a solution of the differential equation dt 2 satisfies the…
A: Given differential equation is: dydt = 12(y2-1) and y(0)=4
Q: determine the general solution to the given differential equation on (0,∞). Q. x2y′′+3xy′+y =0
A: Differential equation: x2y''+3xy'+y=0Now we put a substitutionz=log…
Q: Determine the general solution of the differential equation: y" – 10ky/ + 25k²y = e², with K a real…
A: Click to see the answer
Q: Determine the solution of the given differential equation: (x² – xy + y²)dx – xydy = 0 ; when y (2)…
A: Click to see the answer











